There is a train once an hour that goes straight from Zurich airport to Basel (and vice versa). I would pick that one. Unless you are traveling during peak hours or during a major convention, second class is fine. The middle of August shouldn't be too busy -- a lot of people will be far away on holiday (example: of my seven team co-workers in Basel, only three of us will be in the office in early August. The others will be in South Africa, the Galapagos Islands, Italy and Mallorca).

Buy the ticket more or less on the day you travel. Return tickets cost exactely the double amount always. 1st class is always more convenient. Check rail.ch for time and price.

Are you able to handle your bags yourselves? You'll find (free) luggage carts when you retrieve your bags after your flight that you can wheel to the train. You'll then take the bags with you into your car, up a few steps. Depending on size, stow the bags at the end of the car, on an overhead rack, or, if the configuration of the seats allows, between the rows of seats.

First class is a waste of money which is really unnecessary unless you are very picky people. I'd spend that extra money on a nice meal or a souvenir.