Anyone here have experience with purchasing a central air system for their house? If so, I need some advice about getting quotes, etc.

So I’m moving into my Mom’s house in about a month. She does not currently have central air (or any air conditioning for that matter), and never has. When she asked me to move in some time ago, I told her I could, but that because of several health issues I would need to have air conditioning. She agreed, and we were set to start on the process in late April, but then she fell and was in the hospital and rehab and is just now getting ready to come home.
Knowing we only have a month to go until I need the AC to be in place, she agreed for me to start getting estimates. My time is very limited between getting ready to move, work, and going to see her every day, etc. I managed to squeeze in two people yesterday for quotes, but was wondering how many quotes people typically get. I had very good vibes with the first guy, but not so much with the second guy, who only spent ten minutes at the house, and whose quote was significantly higher as well.
Also, the house is fairly big (three floors and four bedrooms), and I was wondering if a two tonnage AC unit would suffice, or should we go with a three ton unit. Although I need to have AC (our summers are hot, muggy and brutal!), neither my mom or I like it real cold.
Any thoughts or advice people could offer would be much appreciated…thanks!