You may want to give thought to new batteries too. Even if the old packs take a charge you don't know if they are any good unless you have a cycler to test them.
I have been given several trainers over the years and the engine most often found in them is the LA .40. I have used a lot of the cheap LA engines over the years, the .40 was my least favorite, they are/were pretty under powered even compared to there LA .46. The .40s still flew the trainers OK, nothing wrong with them, they teach a student to fly on the wing. They quit making the .40 a while ago. I liked the .46 well enough to use it in my competition fun fly planes. It has a bunch more power then the .40 LA.
As for breaking in an engine. While I was still using the .46 FX I never bothered breaking them in. I just ran a tank of fuel through them and as soon as it maintained an idle I flew the plane. I would do a lot of vertical stunts like the stall turn and big loops, heat breaks in the engine so the engine would heat up on the up line and cool down on the down line. Over the last decade breaking in a new engine has become popular. I only bother with ringed engines.