What would be a good base machine to buy if I'm planning to change all core parts? I will simultaneously purchase a WISE for the tension head, gamma base clamp, gamma fixed clamp, Michal Chudek side supports.
All that's left after that is the turntable and towers! I'd say an Eagnas with straight rails - a Combo 910, maybe. Everything but the turntable and stand is going, after all.
Would definitely avoid Eagnas and go for a Gamma or Alpha machine. You'll end up with a quality machine that you won't have to worry about repairing in a long while. With Gamma, you'll get the base clamps already with your purchase, so you'll save a lot (the good quality base clamps are 400$ + EACH). You should also scout the used market to see if you can score one for cheaper. Reason is, even if you replace a lot of pieces, with Eagnas you'll still end up with a bad quality mounting system (or even straight up misaligned) that you might have to repair/replace in no time.
The Eagnas costs 700$, is there a cheaper way to find a turntable and a stand? technically even the stand is optional. So I should pick the cheapest gamma machine that has a 6 point mounting system?
You need to check the Gamma model, not all of them have the self-centering mounting system, like I have a table-top version and each arm is tightened separately, the posts need to be adjusted manually and will need re-adjustments for other racket sports.