Honestly, it comes down to how much you want to spend. Also, look for one that you can suspend a weight of some sort from the bottom of the center post. The weight lowers the center of gravity and steadies things greatly. All tripods will have a weight rating.
You pretty much have two choices of materials of construction these days. Aluminum and carbon fiber. Carbon fibers is lighter, aluminum (in my opinion) is "stiffer". Aluminum tripods do come in "lightweight" versions, but the ones I've looked at seem a bit flimsy.
If you stick with some of the big names (Manfrotto, Gitzo, Berno, Giotto) it's pretty hard to go wrong. You can go to sites like
http://www.bhphotovideo.com/ and see hundreds of choices and prices. Like most things you get what you pay for.
Then we get to the heads. Stick with a ball head as it gives you the best range of articulation. You'll see the same names on these as tripods. Now you don't always have to have the same brand head as tripod, but unless you're absolutely sure things are compatible it's best to do so.
Personally I use a carbon fiber Manfrotto (I tend to take my wherever I go and weight matters) and a Manfrotto Hydrostatic Ball Head. While you can spend more, this combination seems, for me, to be a good balance of cost versus function versus weight.
Oh, with regards to remote shutter function, some of the newer digital SLR's (I use Canon) now have Wifi connectivity that lets you use a smart phone or tablet to not only trip the shutter but make exposure setting changes. You can get remotely operated tripod heads that allow wireless control, but they cost big bucks.
The good old fashion time delay still works, but it's very clunky compared to what can be had today.