I will be arriving in Milan and traveling by train to Padua (the only train travel on my tour). Should I make a reservation or just plan to buy a ticket at the train station when I arrive? Any other info on train travel would be helpful.
It sounds like you are flying into Malpensa. Take the shuttle bus from the airport to the central train station for the train to Padua. The train from Malpensa doesn't go to that station.
I agree, purchase when you get there. If you will be staying in Milan for a few dyas, you could purchase your ticket on arrival to put your mind at ease.
Since that is a main route, you will have a wide choice of times (see Trenitalia.com) as well as a choice between regional and premium trains. If you are on a budget, choose a regional train, either way, First Class is not worth the cost.