Is Easyjet pretty reliable? Or should I pay a bit more and fly on ITA?
Easyjet is fine. No guarantees at all that ITA will do better arriving on time. However, given what you said about Easyjet arriving earlier, I'd pick them to allow more time to get to Milano Centrale.
How much time ahead would we need to be at the Milano Centrale train station to check in etc? If our flight arrives at LIN airport at 1:30pm, could we make a 2:45pm train from the Milano Centrale station?
It depends on flight arrival time, time to taxi to gate and unload etc., plus whether or not you have checked luggage. I would consider that a bit tight. I would take the earlier flight or a later train, but it is theoretically possible. You only need to be at the train station with enough time to get into the track area (show or scan your ticket and walk through the barrier, almost no time required unless there is a lineup), find the correct track by looking at the electronic display board for your train number, and get on any carriage before the doors close. Since it is a regional train, you don't need to worry about finding your reserved seat, just hustle on board and take any seats.
Same question for the Bologna train station. The flight would arrive at 12:20 and the train leaves at 13:15.
Sorry, I have never flown into Bologna, don't know how long it takes to get from airport to train station by taxi.
I assume I would book the train called ItaliaRail? Are there other trains to consider?
No, ItaliaRail is a third party ticket reseller. Buy your tickets directly on the Trenitalia site.
And yes, there is another option. The Milano Lambrate station is closer to Linate, a shorter taxi ride plus you don't have to go into the often snarled central station area. Just catch a train there and save a few steps. It is a more local train, i.e., more stops than the one from Centrale, so it takes a half hour longer, less the time saved by not going to Centrale first. Also has only one change, in Verona. Up to you, either one is fine. The Lambrate station is smaller, possibly less confusing. Centrale is prettier, in the grand European train station tradition, and has some good food options if you need them. I think it would be a wash.
Italo is the private train provider that competes with Trenitalia only on fast routes. You could take Italo from Milano Centrale to Verona, and then switch to a Trenitalia regional train from Verona to Bolzano. That would be your fastest option and really doesn't add any complexity, the trains use the same stations and tracks. You just can't get all the way through on one provider. And you can't get Italo at Milano Lambrate. See Italo's site for researching schedules and buying tickets here: Italotreno