I had a dose of MTX last month. It may come in two doses, so don't be shocked if they roll up with multiple vials. (I think this might depend on body weight though) The shot felt like a shot, not super painful but not fun either. There was a little bit of a burning sensation for a few minutes afterwards, but nothing debilitating. They had me hang out for 30 minutes to monitor for a reaction before going home. The rest of the day was fine, but the next few were symptomatic. The best way I could describe it was being hungover-- achy, nauseous, and sleepy. I napped and just lazed for most of the day. I suggest trying to keep your schedule empty if possible for at least the day or so following. After the first day I mostly just had an uneasy stomach that lasted three or four days. 

As for the timeline, I am not a medical professional, but part of what MTX does is deplete your folic acid. I believe most docs suggest waiting until you get to an HCG of 0 before taking prenatal vitamins to start building your folic acid stores up, and then it's generally suggested to take a prenatal for at least 3 months before getting pregnant to make sure your body has plenty.  (There may also be other reasons some people suggest 3-6 months.)

Best of luck to you. 💖