Steam login

I don’t know if the current windows computer I have is comparable with wolf quest but I am planning on saving up for a new one. If I made a steam account and bought wolf quest through my phone and then logged in on a new computer would I still be able to play or would I have to pay for it again? Also if I were to try and see if it works on my current computer and it does work would I be able to transfer it over to the new computer once I get it?