I'm going to assume you ride western - and yes those bridles can get confusing at first glance, but a lot of the glitter and ears hoops and browbands are more for show than functionality - feel free to jump in if anyone feels otherwise?
Then the questions come down to what is important to you? And how much time and effort you want to afford to tack maintenance? A good nylon bridle will last years. But they dirty quickly. Good news is a nylon is fairly cheep and come in a variety of colours.
Leather is easier to keep clean if cleaned regularly. But it MUST be cleaned regularly to stay nice. They often cost a lot more too. But usually leather is where you see the creativity come out. This is where you'll see the V-brow bands and the beads and the one ears.
Either can be used for trail riding... but I will suggest ensuring you have a throatlatch if you like to stop and tie your horse once in a while. We have a couple trail horses who learned to pop off their bridles and thus need them.
This is a good example of a basic, simply headstall:
If a horse is prone to rearing, you'll see some riders put tie-downs on their horses as well, which account for the nosebands... although I'm not a fan of tie-downs myself.
Tiedowns look like this:
Most western bridles are fundamentally the same when it comes down to the way they are made to sit on a horse's head, there may be variations in styles, but they all behave relatively the same. So really it's about what you like and what you think looks good on your horse.