Plenty of people “raised right” who can’t keep their homes clean and plenty who weren’t who do. Have a high internal locus of control and realize you’re responsible for yourself, your girlfriend, and for the living beings currently in your home (and any babies you may have going forward). You both can do this.

In your shoes, I’d rehome the cats immediately. It’s not fair to them and you’ll never get your house clean with them there. They’re also an expense you can’t afford and remind yourself of that. Make things easier on yourself by saying you need to learn to be capable on your own before you take responsibility for other creatures. Pare them down to one.

Instead of buying a vacuum now, could you borrow one from family or friends? “Ours is broken” is an innocent enough lie for now. Save up, buy one on Black Friday if you can. Read reviews and don’t just buy the cheapest thing; get something that will last and won’t be a killer for maintenance. Reusable filters are great. Use the remainder towards cleaning supplies and repair work. If you borrow a vacuum, you force yourself to clean it when you’re done and return it. You’re adding a modicum of responsibility to this situation. If someone asks you what either of you want for Christmas, admit you’re saving up to replace your vacuum and would like to get a carpet cleaner down the road. You’re eying ____ model at ____ store and gift cards would be great.

Easiest way to keep on top of this is just to start. Throw stuff away. “I might get to this later” or “I might want this later” aren’t good excuses. Get stuff out of there, get the house manageable, and you’ll find it easier. Effort begets ease.

You two can do this. You’re young, so consider how she approaches this too. If you both aren’t pulling equally then that’s something to consider. Make good choices now as it’s harder to down the road, trust me on this. You both getting on the same page now will make for an easier life when you’re older. You’re definitely at that spot where you can make the choice on how you want your life to go.