If you want to grow veg, pick the veg we mostly import and that isn’t crazy cheap in the shops usually.
We grow blueberries, raspberries, strawberries, figs and various other berries because they cost a fortune.
For veg I focus on stuff we eat in volume - courgettes, green beans, squash. I don’t bother with tomatoes because I buy tinned in bulk and blight got my last attempt anyway. Perpetual spinach also works well for us. I can also sometimes do aubergine.
I can do it cheap because I’m picky about which seeds I bother to buy/try. But think carefully about where you’ll plant - set up of raised beds costs a fortune, so you’ll probably just want to use ground level plots if you’re worried about cost.
Alternatively, just buy chest freezers and bags of frozen veg. Sprouts, beans, broccoli, cauliflower and the like all freeze well
and it’s less hassle (no fighting the slug armies or caterpillars) and still cheap to buy them.