Anything 27" should fit. You have three major choices in this size:
Panaracer Paselas, which ride nice and are light, but have fragile sidewalls
Cheng Shin high center tires, which are cheap, heavy, and durable
Fortes, which are new so no one is sure about them yet (AFAIK
. Chime in if you do,) but they can sometimes be had for less than Cheng Shins
You should be able to get these in 27 1 1/4. If you need tubes, you can use 700c size: Most will say 27" somewhere on the box in fine print.
As for the trailer, any 20" decimal tire (i.e. not 20 x 1 3/4) should fit. This is the standard size for BMX, so you have a wide range of choices.