Tight budget....

I'd think along several lines:

The combination is a nice start with the .22cal over the .410 and a single package means a single purchase.

Unless you have a specific purpose for the .22cal, i would look at a 20ga or 16ga shotgun. That would not be too much recoil but very versatile. You pick the load for what you want to accomplish. Rifled slugs or 00 buck for large game (deer), #4buck or #6 shot for large game birds (geese, ducks, turkey) or (#6) small critters (rabbits, squirrel). #7 1/2 or #8 shot for small birds (blackbirds) or skeet.

Shotgun shells are still plentiful the last time I checked. 16ga can sometimes be hard to find at certain times of the year. I've never had problems finding .410ga or 12ga shells. I've never owned a 10ga so I don't know available those may or maynot be. I haven't owned a 20ga for 20 or 30 years either so I don't know how available those shells are.

.22cal rounds have gotten rather difficult to find in quanties larger than 50 rnd boxes. They are available but one has to search a bit for them.

The costs of ammo has now doubled.