We bought our son’s (will be 8 in summer) laptop used through my husband’s IT department at work. If you know an accountant (from a firm, small or large) or an IT person you could nicely ask if they ever sell their used laptops. Tell the person it’s vital for homework and organization, not mainly for playing video games.
Depending on how kind the person you ask is, the laptop will be from $25—$200.
My son’s cost us less than $50. We picked up another one for a family friend for free, when their ancient desktop died. Both laptops are fine for playing games on. As a matter of fact, my son plays Sims, Sims 2, and Sims 3 on his old Toshiba (probably 8+ year old now) plus the expansion packs.
As for how you’ll pay for it: Go door to door and ask neighbors if they need their garage cleaned out, yard raked, babysit or just go get a summer job.
If you’re not picky, you can get the games used on eBay & save money there, too. I’ve purchased all of our games used and have had zero troubles with them.
BTW: Our son’s been using his laptop since about age 2. He’s been actively using it (weekly, now daily) since about 5.