Hi Dave,
That's one of the really nice things about Linux, it will run on just about anything. My son and I have both done the same thing with old laptops. In fact, we even improved their performance by removing the old 5400 RPM drives and replacing them with SSD's, using the 128GB size as prices are pretty reasonable now. If you do decide to try a SSD, look before you buy to make sure the drive connector is a standard SATA connector. I had one HP laptop with a proprietary drive connector and the nice SSD I bought for it wound up being a spare.
The reason I mentioned the Raspberry Pi is that with a couple of extra MSDC class 10 memory chips, you can try out multiple Linux distributions simply by powering down and changing the MSDC. Small envelopes are handy for keeping track of the spare MSDC's and gives you a place to write notes as to what you have on the chip inside. As long as you don't go overboard adding a bunch of plugins and data, I've been able to use MSDC's as small as 8 GB. Anything bigger works fine and they are pretty cheap for anything 64 GB and smaller.