I think you are on the right track here. The Adire products are very good. I'd still consider the Dayton subs from Parts Express. The same engineer designed most of the drivers for both companies (I believe they are all built by Eminence, by the way). Here's the deal with selecting the right driver. I'm not sure where you are planning on putting this sub, but the size of the box is often a limiting factor for some people. You may have a room to use this thing in that noone will care about, but maybe it's going in your parents living room. Maybe you plan on putting it in your dorm room. Bedrooms and dorm rooms tend to be a little on the small size, so having an enormous box sitting around may not be convenient. I think that just about every 15" or 18" sub out there is going to require a fairly large box, but will probably give you the most low bass output. A nice 10" or 12" sub can give you plenty of SPL in a smaller room like a bedroom or dorm room.
As okc329 mentioned, each driver has a bunch of electrical and mechanical parameters associated with it. Download a program called WinISD from
www.linearteam.com. It's a fairly simple program to use. The drivers you are looking at might be in the database, but you may need to entere the T/S parameters if they are not. I'm sure you'll be able to figure it out. This program will allow you to model the response of the driver in different types and sizes of boxes. You'll learn alot by just messing around with it.
On to the differences in the box types. First, the sealed box is probably the easiest and most forgiving box type. The bass extension isn't quite as good as a ported box, but you'll typically have much better transient response (higher SQ). Sometimes you can run into excursion problems in sealed boxes at low frequencies, but most of the drivers you are looking at have high excursion capabilities, so it shouldn't be too much of an issue unless you plan to use a monster amp. I'd probably recommend a sealed box for any of the drivers you are looking at. Since this is your first project, you are much more likely to get good results with a sealed box. Also, if you put the sub in a corner, you can take advantage of room gain, which has the effect of boosting bass output. With a sealed design, you are likely to get a smoother in-room response, all the way down to 20Hz and below.
The ported box is slighly more complex to build, but not something that is completely out of reach. Using design software, it's fairly easy to get things right. The advantage of a ported box is that it allows a lower F3 point (i.e. better bass extension compared to a sealed box). This looks good on paper, but it's often hard to achieve with some of the drivers you've listed. The current trend in subs is to make them so they can play low and loud in a SMALL box. This is a tough thing for a ported sub, because as the internal volume of the box decreases, the length of the port increases to maintain a given tuning frequency. Also, the lower the tuning frequency, the longer the port. To avoid port "chuffing", you need a large diameter port. The larger diameter, the longer it needs to be. So you often run into problems where the port needs to be 3' long inside a box with dimensions of 14" square. This is where the passive radiator box comes in...
The passive radiator enclosure acts very much like a ported box, but uses atleast one other driver (usually without a motor structure). It is typically recommended that you use multiple PRs (mounted on opposite sides of the box) to balance out the internal pressure - basically to keep the box from shaking around. To tune a passive radiator, you add or subtract mass from the radiator cone. If you want to simulate a PR design, try downloading Unibox from
http://www.pvconsultants.com/audio/frdgroup.htm It's an Excel spreadsheet, so you'll need Excel. I'm not real familiar with PR design, but again, you should be able to figure it out. The PR design is good, but more expensive because you have to buy the passive radiators.
The bandpass boxes probably aren't a good idea. They are relatively difficult to build, and are the most sensitive to errors. Bandpass boxes require a tradeoff between effeciency and bandwidth. To play low, you are going to lose efficiency, and if you want the effeciency, you won't be able to go low. They are probably best suited for the trunk of your car when all you want is loud one-note bass.
To sum things up, I'd probably suggest a sealed box. You'll get plenty of extension, and have a simple box to build. If you don't like it, throw out the box and build a ported or PR version. MDF is cheap!
On to amps. The AVA250 would probably be a good choice. Keep in mind that it's the same amp Parts Express sells for $130. They make a big deal about their SURF filter, but it's really not a big deal. The PE amps don't have any bass boost built-in, so that's not a concern (you can add it if you want, though).
You might want to check out a couple of projects at
http://members.rogers.com/viperoni/Audio/My15DVC/index.html and
http://members.rogers.com/viperoni/Audio/NewTitDVCarchive/index.html Let us know where you intend to use this sub, particularly the size of the room, and someone should be able to give you a better recommendation on which of the particular subs to use, and maybe suggest a box size that would work out well. Also, you might want to check at your local library and see if they have any speaker design books. The best is probably the Loudspeaker Design Cookbook, by Vance Dickason. Lots of info in there.
Good luck
Jason