Hi, cananyonehelpanswer!
I guess most people eat fish for protein and polyunsaturated fatty acids. There's protein in pretty much everything you eat, but some high-quality vegan sources are peas, grains (quinoa, oats, rice, etc.), legumes (kidney beans, soy beans, etc.), nuts, meat analogues like tofu and tempeh and seitan, seeds (hemp, chia, sesame, sunflower, etc.), and non-dairy milk. You can get polyunsaturated fatty acids from flax seeds, chia seeds, hemp seeds, seaweed, mungo beans, french beans, navy beans, winter squash, leafy greens (like spinach), and cabbages (like cauliflower), berries, and wild rice.
You can get vitamin D from mushrooms, but the primary source of vitamin D for most people in the world is sunlight. If you live in an area with low sunlight exposure, you may have to take a supplement or consume fortified foods (like non-dairy milk). You will need a B-12 supplement like this one. If you can't afford or access a vegan source of B-12 then you should still get B-12 from animal sources because you do not want a B-12 deficiency. Trust me.
You should use a nutrition tracking app like Cronometer for a few weeks or however long it takes you to get into habits that regularly give you everything you need.
You'll need a support network so if you don't know a lot of other vegans in real life, keep coming here or /r/vegan for help. We're mostly good people :)
Good luck!
This is a great question and it's cool to see someone acknowledging that a vegan diet is possible on a tight budget. I used to live out of the food bank as a vegan (and still had yearly bloodwork that showed me as all good) so it's definitely possible. My main recommendation is beans and rice for staples. Apart from that, everyone should be eating fruits and veggies where possible anyway (though i am far from a model human here).
My last two recommendations are to find a good vegan multivitamin (or at least a B12 supplement). I use Hippo 7 ($30 per month), but there are others as well. B12 is cheaper if that's too much. And my very last recommendation if you really are shooting for optimal diet (vegan or non-vegan), i recommend downloading Dr Gregor's Daily Dozen app which makes it easier to be a conscious eater. Hopefully this helps, and congrats on your first steps :)
If you're going vegan, B12 needs to be a priority, but it doesn't need to be expensive.
Just for reference this B12 Supplement is
~$8 for a 50 day supply
But each "dose" provides like 125,000 % of your daily B12.
If instead of 2 gummies a day you just took one (still yielding 62,500% of daily B12) you'd be paying $8 for a 100 day supply which comes out to about $2.40 per month.
I obviously don't know your financial situation, but this is genuinely one of those situations where its the difference between buying one less coffee a month to finance your b12
Hope that helps