Can I use a 2007 iMac as a display for any other computer?

The "why" is in the hardware and software requirements for Target Display Mode (TDM) shown in this Apple support article:

Use your iMac as a display with target display mode - Apple Support

2007 iMacs never supported TDM.

Unfortunately, you cannot use the 2007 iMac as a display for any other computer.

Since funds are limited, I think your best option is buy a refurbished Mac mini direct from Apple (or other respected Apple reseller). A new monitor can be purchased for ~$100 or so. Continue to use your current keyboard and mouse.

Please visit > https://www.apple.com/shop/refurbished/mac

At $589, this M1 Mac mini is the lowest priced Mac on the list at the moment.

https://www.apple.com/shop/product/FGNR3LL/A/refurbished-mac-mini-apple-m1-chip-with-8%E2%80%91core-cpu-and-8%E2%80%91core-gpu?fnode=cfb1bd20ba86aeedd6a2ddd4f3d4ab698db346d4e3ef9dc9954db6f6c0b7d53f8e636049b871fb3ce84a8f30408777d10a0fc64991651480a173bbba4181cf94f3e5a7a84dee82e9045dff8873123e9f

It only has 8GB of Unified memory. That's a little thin in my book, but it'll get the job done today for the limited use you describe. Others will likely have a different idea of the Mac mini you should get. I rarely recommend the lowest tier of any Mac - or anything else, for that matter. I'll usually suggest a step up for the sake of a wee bit of future proofing.

Macs come and go from the list constantly. If there isn't something that pushes your buttons now, look again tomorrow or in a few days. Your planned use is not demanding at all, and any Mac can do those things.

I had a Mac Mini M1 with 8GB RAM and it ran great even doing some video rendering. RAM on M1 Mac is much more efficient than RAM on Intel Mac. You should be fine with the 8GB and I would get 512GB SSD.