You've mentioned cheap ammo a few times. 22 ammo is as cheap as it comes.
I know you dream of something bigger but a 22 is a great "first rifle." It is more than a rifle, it can be a major factor in developing your shooting abilities. Stick with me...
Friends and family come down to my house all the time to shoot rifles and such. I have a nephew that could not hit the broad side of a barn at 300 yards. So the next time he came down I tried to get him shooting better by him and my brother taking turns at 100 yards with the 30-30. He was hitting almost every shot.
Next we moved back to 200 and he hit one or 2 then started missing again. I noticed he was rubbing his shoulder ever once and awhile. I then noticed he was jerking the trigger. I tried to get him to squeeze the trigger but it was too late, he developed a flinch and no stressing of how important it was to squeeze the trigger was helping.
I went to the house and grabbed the bolt action 22lr and we went back to 100 yards. The first 5 shots he missed from the flinch, but since the kick wasn't there he started to trust in the squeeze. The last 5 shots he took were all hits.
I then bypassed 200 for one shot with the 30-06 at 300. He hit it. That was maybe his 20th shot with a high powered rifle and
All due to the use of a tool; a 22 rifle.
Go find a used 22 rifle, or at least the cheapest one you can find so you can first get used to the bang, before you go for a boom with a kick.