And any job will level you up. Doesn't matter which one.
This is not entirely correct. Doing any work will earn you 1 XP per hour. So it'll take days/weeks to earn enough XP for a new class if work is all that you do. Also, each task has an associated stat (PHY, WIT, SEX) that it will, very slowly, improve. To gain stat points quickly you have to use the stat in combat (or in bed, in the case of SEX). You also can gain as much XP from two fights in a dungeon than from manual labor back at the mansion for an entire day (and time does not pass while you are exploring the dungeon). So, yes, you can play the game slowly and grind XP without any risk at the mansion. Or you can blitz through the game by farming dungeons, one after another after another. Very different play styles. Which the game supports because, even though there is some time pressure, the requirements that the game sets can be met no matter what style you prefer to use. But you do need to learn how to optimally employ your chosen style. The game will punish anyone just fumbling around trying to figure things out. Don't despair if your first few games result in failure. Learn what does and doesn't work and try again. What races you choose for your first two character, and especially how you build them, will make an enormous difference in how hard the game will be. Add to that the fact that the RNG's selection of your first 4 guild quests can vary drastically, and some of these starts are very easy or very, very hard to complete in the first week.
Regardless, you have 13 and a third days to come up with 1000g (by 0800 on day 14), which works out to needing to earn an average of 75g a day, or a tad more than 3g per hour. This is easily achievable by prostitution. Or for those that have moral objections to whoring your characters (which is odd, given that you don't seem to mind being a
slaver) you can also succeed just by fishing. Just one person fishing (the max you can have unless you upgrade your fishing) should be able to net (pun intended) 1 fish per hour, which is worth 3g at market (which is the amount you need per hour). Your other character can go to another town and fish or hunt (or gather wood or whatever) there to supplement your passive income by selling what they gather. It's slow, but it's also 100% safe.
That's two of the ways to meet the main quest's first deadline and neither involves any fighting at all, nor does it matter what your characters are or how they're built. However, carefully choosing your character's races, classes, and allocation of stats can significantly boost even this sort of passive income. If you're going to go delving into dungeons, however, you will have to be much more thoughtful in how you create your characters. Or the game will hand your ass to you.