Wine is a utility which allows you to install Windows applications in an Ubuntu environment. However, Wine takes a lot of resources from CPU and will leave you with games that run slowly or hang. This I am saying on the basis of the configuration you will get in your budget.
I have a laptop with 4 GB RAM, Intel i3 2nd gen and in this, you can't run anything using Wine leave alone games.
Doesn't matter laptop or desktop.
Unless you intend to play games that run only on Ubuntu, which are not that many, to be honest.