What mods to download and girlpacks to setup the game for a "complete" experience.
Honestly, there's no right answer here, it's different for each person. You need 20 girlpacks for Scramble and 35 for Crown Jewels, but beyond that, it's just purely according to your own personal preference.
Also, should i load all the girl packs before starting a new game or can I load them later too without issues to continue the game?
In my very limited experience, there can be mild issues with loading them later. I had one run where I added in some girlpacks as I went along. Eventually, I reached the point when the recruitment screen was empty, even though I didn't have all the girls yet. It seemed like the ones I added in later were the ones that were missing. However, I was still able to pull them from Lottery, so it wasn't a huge deal.
At this point, I pick a lineup of about 100 girlpacks before I start a new run and don't add more, just to make sure something like that doesn't happen. Still, it's not really a huge deal, it might just be that the girls you add later don't show up in the recruitment screen (which would also be true if you didn't add them in the first place). I'm not aware of any incidents where adding new girlpacks in the middle of a run causes the game to crash or corrupts your save data or anything major like that.