I love these questions!
Eric, we were all in your shoes at one time. Everyone on this board is very helpful and will be happy to answer your many questions. It sounds like you have more than enough time behind a wrench to dive into karting.
I won’t dive into the subject of which kart you should buy, but you did ask about shifters. yes you *can* start a shifter by yourself by push starting and jumping in. It is much easier if you ask the guy pitting next to you to give you a push, though, and then drop it into gear and motor away. Almost anyone will do it. The TaG advantage is the push button starting.
As you know from other forms of racing, the initial purchase is only the BEGINNING of your expenses. I also think you should reconsider your thoughts about not racing. Lapping is fun for a while, but local club racing can be affordable and quite a hoot.
You may want to draft a buddy to come help you in the pits until you get the hang of everything. Or, better yet, have a local karter help you and look over your stuff.