Slax will certainly run on that computer: it's fine on this, with 1 GB and an AMD Sempron. Wine is available: you download the module from their website, click on it in your file manager, and it's installed.
Puppy is an alternative and that too has Wine. You install it in the same way, from a Puppy .pet file.
It's some time since I tried Porteus, and I had a few problems with it.
For what you can run in Wine, look up each program at https://www.winehq.org/