It's always best to use a cable over WiFi for any installation. Personally, I have installed Linux many dozens of times on many different computers, and never once had a WiFi issue. Generally you find missing driver issues for the latest, greatest pieces of hardware. Once you're installing Linux on an "older computer", you just don't see problems. At least that's been my experience. I have had more issues trying to install Windows than trying to install Linux.

Most Linux distros can run off of a CD or thumbdrive. Then after you've tested like that to see that everything works, you can tell it to install on your hard drive. Do not judge the speed of Linux based on running it off of a CD or thumbdrive however. Those are way slower than a hard drive. And ridiculously slower than an SSD. A lot of Linux distros can be booted off of a CD/thumbdrive and instructed to install totally into RAM (you need to have a lot of RAM to do this). In that case, Linux runs like a scalded ape! Of course, if you power down the computer, everything in RAM disappears, so running 100% from RAM is really mostly for testing or specialized applications.