I do WW Core. I find that once you build up the basics, my grocery costs seem to be less.
Hope you like beans, white, black, red, pinto, etc. If you have time, you can cook from dried beans. If not, usually store brands of canned beans are cheap. You can use a little bit of lean ham as flavoring if you like. Brown rice is cheap; again if you have time, buy the kind you have to cook at lot. Of course on Core you limit potatoes, brown rice and whole wheat pasta to one meal a day. but no limits as to how much if you're eating enough to satisfy your hunger. With the brown rice, if you cook a lot at one time, it will keep a few days in frig, just nuke it. You could add sauted chopped onions, garlic, chicken or beef bouillion. Makes a nice rice pilaf.
I buy store brand frozen veggies- around here they are cheap, like $.89 to $1.00 for 1 lb bag. I'll cook a whole bag at a time. I'll make veggie soup or add leftovers to salads. Eggs are a good nutrition staple. Cheap protein. You can make omelets with salsa or other veggies. Use canned fresh or frozen veggies. Make sure no added fat. canned tuna & salmon are good too, if you like them.
Oh yeah, can't forget oatmeal. Buy the kind in the big container that cook for one minute. Makes a breakfast that will stick with you.
That would get you started. I certainly know how to eat cheap. I lived about 6 months on Ramen noodles, cheese, eggs & beans & rice. It's do-able without putting on weight. Good Luck.
If I can help you with anymore Core advice, PM me.
