What are some must have specs in you opinion to run most modern games
There are none. Choose the best ones to fit your budget.
would you have a #1 recommend for a prebuilt to get started with?
I don't really recommend prebuilts. If you look up reviews most of them are just awful. But iBuyPower seems to have a decent reputation. The Steam Machine will be available sometime next year but its a relatively underpowered machine built for the living room. Not sure what your budget looks like or how you plan to play but that could be a good option. However it should be noted that it's not upgradable. I've saved buckets of money by upgrading my PC over the last 20 years.
As for distros, there is obviously no "best". The most commonly recommended one for beginners is Linux Mint. I recommend Zorin. If you want the best possible gaming performance, you could go with Cachy. It's also available with Steam's "Game Mode", which will give you that handheld/living room experience.