I sat down one night and looked at a ton of supplement nutrition info, and looked up stuff on webmd. I know your question was in regard to a super tight budget, but I'm going to just info-dump in the hope that the info is at all useful to anyone.
Multivitamin - the best one, by my standards*, that I could find was Nature's Bounty Multi Day Plus Minerals. I'd give a link to the Amazon page but I think that's prohibited. I find lots of Nature's Bounty stuff in stores, but this particular supplement I can only find online. It's by far the best supplement I could find, even within the NB line.
* - as little as possible being over 100% of recommended, and with as much variety as possible
Biotin - Haven't noticed much from this yet, though it may be contributing to my skin. The hair and nails haven't really responded the way I was hoping, I may need to increase my dose.
MSM - This made my joints awesome. When I first started taking this I actually had a lot of discomfort (I made a post about it at the time, but hadn't put it together as being related to the supplement. I tend to be really sensitive to change and the effects of drugs...) But after about a week it was all good and now my joints are better than ever. May also contribute to skin, and I think it either spurred some alignment changes of my skeleton or coincided with them.
Fish oil - Increased my good cholesterol levels to the point my doc got really happy and quit bugging me about it. I may switch to flax seed oil as I think it has the same omega-3 stuff and no risk of mercury, no fish taste, no squeezing of the fishies for their precious oil, etc.
Evening primrose - Contributes to better skin and has some other potentially nice effects.
Vitamin D + calcium - this was recommended by a psychiatrist to help stabilize and improve my moods. Also helps to retain bone density, I imagine?
Magnesium - I don't need this nearly as often now that I have a decent multivitamin, but I still find I need to take this maybe once or twice a month or my muscles start being even more useless than usual.
Cranberry juice - I forget why my friend recommended it, but this stuff is the nectar of the gods! Drink some. For seriously. Stomach problems I had since starting HRT that kept getting worse with every dose increase and when adding progesterone were magically fixed in a way that fiber supplements couldn't come close to. I guess it does other stuff too. Huge source of carbs though...I've been told there are cranberry pills? Can I just get all my nutrition from pills? It would be a lot easier than the whole eating thing tbh...