One other note:
IF you had a thunderbolt 3 port on your laptop, you would have had an option for an external GPU for said laptop using an external GPU enclosure. BUT, since your laptop has AMD inside, I'm pretty sure there's no thunderbolt 3 port incorporated.
Laptops in general aren't ideal for rendering to begin with, due to the amount of heat that rendering often generates. So as you noted, a desktop system might be better. You can make do with a laptop, and a number of people do, but your goal should be a dedicated desktop rendering system. You'll be happier in the long run.
If an external enclosure were an option, then you'd need to shop for one with an adequate power supply for whichever GPU you ended up buying for it.
As others have noted, more physical system ram would be helpful, even for your laptop. 16 GB is a comfortable minimum, 32 GB is usually more than adequate. 64GB is generally overkill for Daz Studio, but if you can afford it...
It looks like you are now planning on a desktop system. Right now, older 8 core Ryzen chips are on sale for fairly cheap, and of course there's the newer 3xxx series Ryzen chips. The Ryzen APUs max out at 4 cores at the moment, but the 8 core APUs (4xxx series) are supposedly coming down the pike fairly soon, and may be announced within the next couple of weeks at CES. It may be a bit before they become available after said announcement though... And of course there's the Intel chips too..
The 8 core APU is an interesting option to consider, because it includes the Vega graphics, hence not requiring usage of the first PCIe 16 slot. Similar to the 2400G/1080 Ti setup I'm using. Otherwise, if you have the extra x16 slots available, buying a cheaper GPU (AMD or Nvidia) to drive your monitor, and a second, larger card for most of your Iray rendering needs is also an optiion. This isn't required, but if you plan to use your system for other things while a render is baking, you'll appreciate not having your 'monitor' GPU focused on rendering while you work.
Intel already has 8 cores with integrated GPUs with some of their larger i series CPUs. Intel integrated graphics are unimpressive to begin with, but more than adequate to drive the Daz non-Iray viewport modes and your desktop. But if you also game on your system, yeah AAA gaming on the Intel integrated graphics might be a bit painful...
The reason I focus on AMD CPUs and APUs in my discussion is because they are in general cheaper than the comparable Intel options. And in the case of the APUs, yeah AMD Vega (in the 2200G/2400G/3200G/3400G) is a pretty decent solution. Intel gurus are free to chime in here of course!
Since renders do drop to CPU only occasionally, sometimes it's easier to just take a break while the CPU crunches away at some render, at which point more cores are helpful. But if you have a decent Nvidia graphics card, and are doing Iray renders, you should probably look to optimizing your scene so that it can fit in the graphics card memory.
As for storage, in this case HDDs are fine, but of course SSDs are a bit faster. Since it sounds like you are just getting started, 2 TB of storage might be a comfortable minimum, but if you end up acquiring a lot of Daz assets you'll eventually want more. If you install your Daz assets onto a separate drive, say an external one, this will make it easier to move your assets to a new system later. Of course, you'll have to let Daz know where you've installed them. You can just go with the 'default' install on the C: partition in the user folders of course, but when it comes time to transplant your Daz install into a new system, it may require a bit more work to do so.
Faster SSDs are great for things like booting your operating system, but as far as loading Daz assets into a scene, you won't notice a huge amount of difference in loading times if they are installed on a HDD. So if you are on a budget, a decently large HDD (say 4 TB or more) can be found for fairly cheap, and those are also useful for such things as making backups for your Daz install, if you end up using an internal drive on your 'new' system as well.
So, to recap, if shopping for a new system:
IF you prefer Daz iray, get an Nvidia GPU with the most VRAM that you can afford. RTX 2xxx cards are a bit faster, but the GTX 1xxx cards work too. The earlier GTX cards (if you are buying used) are often options as well, but will be a bit slower in most cases than the newer cards.
The CPU is a bit less important UNLESS you are doing CPU only rendering, say with 3Delight. The older 1xxx and 2xxx series Ryzens are a bit cheaper right now. The 3xxx series Ryzens are faster. If you are on a budget, a 6 core Ryzen 3600 is an interesting option, otherwise I'd suggest the 8 core 3700 just for all around usefulness. The 2700 and 2700X 8 core Ryzens are also interesting options, but are of course a bit slower than the 3xxx series Ryzens. Again, this will come down to budget.
2 TB of storage in your system should be a comfortable minimum, with an eye out for a 4TB+ HDD later on once you get settled in and start making backups of your Daz install.
16 GB of ram if possible, 32GB would be better. 64GB is probably overkill, but can't hurt if your budget will allow.
R.E. a motherboard. If you are going to be doing a LOT of rendering, say for a game, I'd look for a motherboard with 3 or 4 'double spaced' PCIe 16 slots. That way, you can add a second, third, and maybe even fourth GPU for rendering later. Multiple GPUs will generally decrease your render times by roughly half, 2/3rds, etc.. IF you are doing Iray renders and the scene will fit in the smallest card in question.
As a theoretical, if you were mixing say a 6 GB 1660 Ti with an 11GB 2080 Ti, both cards will crunch the render, if the scene will fit in the 6 GB card. Otherwise, Daz will ignore the smaller card. Daz Studio does allow for usage of different cards in the same system, even from different generations to a point, but if possible, using similar cards will probably be better, although more VRAM is more important particularly if you like building larger scenes. There's a Daz Iray benchmarking thread on the Daz forum where several results are obtained using a mixture of cards.
Do keep in mind that a decently sized power supply is important, particularly for multiple GPU setups. These days, even 1200-1600W power supplies can be had for fairly cheap, but of course pay attention to the reviews as not all power supplies are created equal.
FINALLY, the Threadripper discussion. Or perhaps Intel HEDT CPUs. The high end desktop systems in general have more PCIe lanes available for cards, storage, etc. For rendering, though, even if you aren't running your cards at full speed (x16), x8 or even x4 may be adequate for your needs. I'd suggest x8 as your target though, for slightly better performance than x4. I've seen a couple of mentions of some graphics cards not liking x4, but that's another topic. Anyways, the older Threadripper chips are dropping in price, and most Threadripper boards (not all necessarily) can comfortably accomodate 3 'double slot' GPUs. So even if you grabbed a lowly 8 core 1900X Threadripper for budget reasons, it's an interesting option.
Intel X299 is similar, and the new 10xxx HEDT CPUs are agressively priced vs. the older Threadrippers, if you can find one, so these might also be an option. It'll all come down to price and 'bang for buck' here.
For most people, though, an HEDT system isn't necessary if you are just getting started out. It'll all come down to how much you can set aside for your new system. You may end up spending almost as much on the Nvidia GPU as you do on the rest of the system, so be prepared for that, unless you go for a smaller GPU or something... I'd recommend focusing on the larger cards if you are planning on Iray though.
As for a monitor, well 1080P should be the minimum you consider, 4K is better if you can afford it.
One final thought. Even if you do end up buying a dedicated desktop system, that Acer laptop isn't completely useless to you. You could use it to put together scenes on the laptop while the desktop is busy baking renders. You'd have to transfer your scene .duf files over to the desktop once you are ready to render them, and of course would need to install your Daz assets on both, but it's an interesting productivity option for you. USB sticks are good for moving .duf files around between systems of course! Or a networking cable maybe...
If you have the 'multi GPU' setup I've been suggesting though, with a 'dedicated' GPU for the monitor and separate Nvidia card(s) for the Iray rendering, and can open multiple Daz instances, you may be able to work on other scenes just fine on the desktop system while rendering as long as the renders aren't 'CPU only'. Just suggesting options here.
Daz did make a change with 4.12 apparently that disrupts opening multiple Daz instances, but a number of people have complained about that, as they were doing the 'multiple instances' thing. Not sure if it's been 'fixed' yet, as I'm still using 4.10 on my rendering system. Long story...
Hopefully, all of this is this helpful to you in putting together your shopping list...