So I want to trail ride

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! ;)

Enjoy.

Always best to ride with a buddy. Go with the neighbor even if that horse doesn't like to lead, it's good for them both. Ask around, join a trailriding club if there is one locally. If you must go down the road, stay on the unpaved area as much as possible - riding with shoes on pavement is like iceskating on horseback. If they slip, they really slip. I like the suggestions of what to bring, but I always like to ride on trails with the halter on under the bridle, and with a lead attached. It's a good back up if one of the horses balks at something - the other can pony them on through if they refuse to just follow, and if you need a break along the trail, you have a way to tie them.
Take a small bag, purse, or saddle bag to keep a bottle of water and extra fly spray in, and keep a cell on you (not on the horse, in your pocket). That's about all. Have fun. It's good to change up the horse's routine.