I had a sinclair 1000 when I was a kid. http://oldcomputers.net/ts1000.html Yes, $100. NOT a rich family's computer.
Eventually, I got a Commodore 16. $100 also.
Then, when that died and I was crazy about it, I got a Commodore 64. $600. Well, -I- didn't get it. The family did. I had to share with my sister and mother. (Dad didn't care.)
Eventually I got my first IBM-compatible. Again, shared. It was about $2500, if I remember correctly. This was about 10 years after the first computer our house had, I think.
I didn't have other hobbies. There were no expensive lessons or instruments to buy for me. Video games? Atari 2600, then 7800 that were bought used and dirt-cheap.
No, you don't -need- to have a wealthy family to get into programming early.