First off, if you haven't read the sticky at the top of the page that lists trainers, do that. I'll try to make it simple for you though, because this is just how I think of it. You have traditional trainers, sport trainers, and sport planes. If you are working with an instructor any of them will work, especially since you have some flying experience. Basic trainers are the flat bottom, high dihedral jobs that we've been using for decades. The differences between them are fairly minor from what I've seen, with a few being a little lighter and a few being easier to fix, etc. Sport trainers have less dihedral and semi-symmetrical wings. They are better in the wind and fly vertical lines and inverted better at the expense of not being as quick to self-correct. An example is the Hobbico Avistar (the hands down favorite at my windy club). Sport models take it a step further, usually with symmetrical wings and close to neutral handling, but still stall resistant and really good in the wind. The venerable old Ugly Stick is the quintessential sport plane, with the Sig 4 Star a close second. If you want someone to narrow the choices down to you to the best ARF of each class, my answer would be the Sig LT40, the Hobbico Avistar, and the Hangar 9 Super Stick.

As for radios, Futaba, Hitec, JR/Spektrum (same company) and Airtronics all make quality units, although if you do some searching you'll find lots of anecdotes of Spektrum equipment having mysterious failures. But they are also the market leader so it could be a simple case of the law of averages. Figure out exactly which Lancaster you'll want to build and how many channels you'll need for it, and pick a radio from any of those 4 that does what you need it to.

You also asked about field gear, and frankly it doesn't really matter. A 12/24 volt brushed electric motor with a cone on the front isn't hard to figure out, so get the color you like. I will recommend though going with a battery pack attached to your starter instead of using cords. It makes life easier at the field.