It doesn't matter really if your neighbour's horse doesn't like to lead. Just having another horse that is calm will help.
It is impossible to acclimatize your horse to everything you will come across. Your goal is not to desensitize the horse, but to develop trust. Your horse must learn to rely on your judgement to a great degree. If you say it's OK, then he should believe you. (Exceptions to every rule though; if a horse that usually crosses a bridge decides one day he won't there is probably a reason.) Bring lots of funky things to your horse and walk him up to lots of other funky things. Have others do things near you and him. Whatever you can think of. Again, the goal is for him to be secure with you so he looks to you for guidance.
Your number one concern is safety; number two is comfort; number three is pleasure. Safety includes bringing stuff along as previously posted, telling someone where you are going, health of you and your horse and ability to control your horse in lots of different situations, environments and terrains.
Distance -- if you ride at least once a week already, you're good to go for at least a couple of hours the first time. Horses can maintain a walk for a very long time. If the terrain is very hilly, twisting or rough, you may want to consider spending only 1/2 hour on that terrain and the remainder on something easier until you are BOTH ready.
Oh, and yes, definitely you can trail ride English. Go whichever way you feel more comfortable. I started trail riding English and am only now reverting back to it again for training purposes. Your horses trained in English will be fine in Western as long as their basics are good. My horses go both ways! ;)