I bought a Optiplex 9010 for ~100€, + a monitor for free. You want to look for ones that are sold by schools/businesses, they'll usually be sold in a lot, but if you contact them, you may be able to get a single tower by asking. If you buy one from like Ebay, you'll most likely be buying it from someone who bought one of those lots, and is reselling them, so you'll end up paying more.
What I want to note, is that even the mini-tower models are quite small, and if you do decide to go for a beefier GPU, you need to make sure it's not too long (I ended up chopping off my HDD bay).
Also doing bigger upgrades (such as new mobo, new case, or smth like that) is difficult and you need to do them at once since Dell uses proprietary stuff for things like the power button and USB ports.