Fly rods: Obviously, if you're fishing on a small stream with a lot of brush & tree cover, a shorter rod would be helpful. How long, or short, your rod should be is relative to the length of rod you normally use most. If you usually fish with a 9ft rod, than going down to a 5ft rod might not be very comfortable. If you're used to a longer rod than stay with a rod that still has some length to it. On small streams that have a lot of cover & obstacles close by to get snagged on, I generally won't go with a rod over 8ft long. I normally use rods between 7 & 8ft in length on smaller streams, but there are time when I wish I had brought a shorter rod. Because you'll be trying to avoid all the places there are to get tangled in on a small stream, your best bet is to go with a rod who's length your're comfortable with, but still short enough to enable you to work in tight quarters.
No matter what length of rod you go with, I recommend always using the same length on really tight streams. The more you use a rod of a particular length, the more you'll be able to know where the rod tip is at all times. You'll become so accustomed with the distance the tip is from your hand, that it will start to feel like an extension of your body.
If you're fishing a smaller stream that flows through a wide open area, like a pasture, etc, you're going to want a longer rod. In these conditions you need to stay back from the water, lest the trout see your shadow or profile. Having a longer rod with a slightly faster action will help you keep your distance while still delivering your line where you want it.
Fly line: Sure, you want a good quality line to use. However, you also want a line that can take a beating When you're fishing on most smaller streams your line's going to get snagged on roots, branches, etc. You're going to be casting it over & onto rocks & sand. You want a line that can stand up to all this & more. I would suggest leaving the expensive, hand-made silk line at home for this type of fishing.
Leaders: For all the reasons listed for fly lines, you're going to need a stronger, stout leader. I usually end up balancing the leaders strength wit it's diameter. You want a leader that will hold up to the snags, & debris that will effect it, while still being fine enough so it doesn't cause you to miss fish. Use your best judgement for the conditions you're in.
Weight & floatant: Make sure you have both of these. If fishing below the surface, you're going to need to get your fly down as quickly as possible in the short distances between you & the trout. I recommend having a good supply of split-shot sinkers with you, in size "bb". If you want your line to float, you'll probably be needing to reapply line dressing often. there's a lot of algae, moss, & other stuff in small streams that will stick to your line & weigh it down, causing it to sink.
Overall: Go as lightly as you can. You don't want a lot of stuff weighing you down. Sunglasses hanging from your neck, a net swinging on your back,.....these are all things that can get you hung up & stuck in the bushes & thick undergrowth. Believe me, there's nothing much more embarrassing than the sting & pain from your landing net as it's pulled from a branch, smacking you in the posterior!!
Do dress for the weather. If you're fishing a mountain stream in higher elevations where the weather can go form one extreme t another in minuets, having a variety of clothing with you can save the day.
No matter where you're fishing, you want to be as mobile & free as possible. If there are tackle items you always carry, but seldom (if ever) use, leave it back at the car. When you're stuck deep in a brier patch, struggling to get free, you'll be glad you did. I know. I was once carrying way too much tackle when I was stuck in the briers & stepped on a bee hive. It didn't end well. However, I did make it out of there fast enough to make Houdini jealous. I can't say I was glad that I had all the extra equipment with me on that day!!