Sorry about the wall of words that this is probably going to turn into. I would like to make a distinction between several parts of the system. A tripod is really several parts, that have started to be touched on here. The most obvious part is the legs, then the head, and I'll also throw in the clamp (since there are some options available there). Also, since you specifically called out wanting to do vertical shots, I'll add one other item - an L bracket.
So the legs are the base as you already know. The head on the lower cost tripods usually comes with the legs. Usually included with the head is the clamp/quick release clamp, however you can always remove the head from the tripod and put another head on (as it just screws on). The clamp comes in a number of various mechanical interconnect styles that determines the plate style/type that is used.
- Legs - This is the bottom part, the legs. There are usually three of them. Aluminum or Carbon Fiber are usually the options to choose from (but there are also some very fine wood versions available). There are also flip leg locks or twist locks as an option. Weight is a consideration - heaver is also better, but for traveling weight and size is a consideration. Number of sections - usually 3 or 4. Less is more in this case as fewer sections make a stronger base, but more is better for traveling and carrying it in luggage. With or without a center column is also a choice. With a center column and actually using it, you can get some movement, however for us taller folks it does make it easier on the backs. Legs run from $100 up to $1000.
- Head - Chris talked a bit about the heads. It really goes to what you are shooting. 3 way heads are great for video, while ball heads are great for stills. When you need fine control in setting up a shot 3 ways are a bit better since they afford control in each axis. There are also geared heads that are good for macros and just general night sky shots (wide field astro-photography). On ballheads you really need to look at the manual user controls. A main knob is primary, however I think you will find that a friction control is also nearly a must. I came across one head that only had the main knob without a friction control and it was nearly impossible to use. If you are into doing panoramas, then a panning ball head is really nice. The problem is that most manufacturers put the panning mechanism in to the base - this makes sense until you realize that for this to pan level, your legs need to be very level. Personally, I like to plop the legs down and level with the ballhead itself. So this requires the panning table to be above the ball and essentially part of the clamp assembly. Heads run from about $100 to $400+.
- Clamp or Quick Release (QR) Clamp - I broke this out separately since you have a choice here. ArcaSwiss (AS) is both a brand and a standard. They are more high end, but very much worth it depending on your amount of usage, and inter-comparability with other parts. A clamp and plate are essentially a system. There are several clamp styles - the ArcaSwiss as a standard, then there are the others - the screw that screws directly into the base of the camera - or several other styles of plates (Manfratto being one with their RC2 style) that have smaller followings and are usually manufacturer specific. Clamps usually run $50 and up
- Plates and L Brackets - Plates attach to the bottom screw hole assembly of the camera and remain attached to the camera serving as a quick way to mount the camera on to the tripod system. The plate attaches to the clamp.The L bracket below is a type of plate. I bring this up since you are calling out vertical shots. To easily flip the camera between landscape and portrait orientations in mounting an L Bracket is really nice. It is really an metal "L" molded to the body of the camera that has two plates integrated in to each side of the "L", thus allowing you to flip the camera and then easily and quickly tighten the clamp that is holding it. L brackets run at about $100 to $150 (and are getting increasingly more difficult to find for Pentax bodies). Individual plates run from about $20 to $50 depending on style, type and make. AS type equipment is made to be interoperable thus interchangeable
I never realized before I started photography that mechanical support can be so &%#@ expensive. The reason why I broke all of this out, is that your need for vertical. You can do it easily several ways. By far the easiest is with an L Bracket, but you can also use a ball head with a notch, that allows you to flip it to the side and there by act as a gimbal. Or you can do both in conjunction with one another. I really only know of L brackets coming with AS type plates. Another approach is to use the 3 way head which allows you to separately control the vertical and horizontal motion or pointing. An L bracket here would also work well in terms of easily setting up the camera in portrait or landscape.
What have I forgotten. All of these parts are available separately, or usually all come pre-packaged in the lower price units (you just usually don't think about it - but the choices are essentially made for you).
I bought a light travel tripod [Benro travel angle] (it fits nicely into my carry on luggage), and then later found a heavier Manfratto [3001]used to keep in the back seat of the truck. The Manfrotto came with a head 486R2 that I hated. It required three hands to operate (one to hold the camera and two to work the quick release safety latch to remove the camera/plate from the legs/head).
I splurged on a Acratech GP head - way more than what I ever wanted to spend (but I saved up). It has turned out to have been worth it. Its an AS type of head with clamp/plate assembly that inverts to provide the panning turntable functionality on top of the ball.
I have had two Kirk L Brackets (AS type) since they are fitted to the camera body (one for my K20, and another for my K5). The K20 did fit on the K5 but with the K20 being a larger body, it did not fit as well as I wanted, so I finally broke down and bought the K5 specific L bracket. The L brackets for the specific Pentax bodies come out after the body is introduced and usually dry up near the end of the body run. My L bracket lives on my body. It makes it ever so slightly heavier but I tend to use the tripod quite a bit.
hope that helps...