Having built LOTS of speaker cabinets over the years I will NOT use MDF for anything.
Some say MDF is acoustically dead, it is cheap, you can veneer it. But the drawbacks are too great. It crumbles easily on edges. The lightest bump and corners and edges are damaged. It does not hold screws well. And it is WAY TOO HEAVY for large speakers. For tiny "monitor" type speakers, MDF is barely acceptable.
Regular construction plywood is too rough, the layers not glued well enough.
Don't even bring up the subject of particle board.
The best material I have found in about 35 years of building speakers is birch veneer cabinet grade ply. As far as resonances, flexing, that is taken care of in proper bracing. It holds screws well, cuts precisely, and the veneer is easily stained and can be finished to look quite good. The cut ply edges may be covered with birch tape (veneer on a roll made for edging).
Carpenter wood glue (yellow glue) is excellent. Glue all joints.
I use 1"x1" bats in all the inside joints, with #6 drywall screws. I glue the joint, drive in the screws from the inside. The screws hold it tight and allow continued construction even with the glue wet. Wipe way all excess glue on outside surfaces with a damp cloth. This is so later when you stain the stain will penetrate and not leave a light spot where glue was.
Using this glue and screw method no clamps are needed, construction can be done quickly. For places where you can't get your cordless drill driver, you can use small nails... just make sure they are not long enough to go through both the bat and ply, to the outside. These are just to hold until the glue dries.
Don't underestimate yellow carpenter's glue. I made a box once and then destroyed it just to see how well it would hold. I had to really bang on it with a 10 lb sledge hammer to break the joints. What I found was the glue did not break.. the wood did. The carpenter's glue is stronger than the plywood!
Or use whatever construction method you wish. If you want to route grooves, that is fine, too.
Unless absolutely necessary (some horn designs) I never make a removable back or access panel. I do all wiring, crossover installation, etc, through the woofer hole. The last part of assembly is dropping in the woofer.
After the glue dries you could remove the screws if you wanted. That stuff is strong!
After the first gluing dries, go back on the inside and apply another bead of glue all around. This will ensure a good airtight seal.
For some pro audio spkrs I cover with carpet. I use Ozite (as do many manufacturers) which you can buy in convenient size rolls at Walmart in the automotive section. 3M77 spray adhesive is the way to go on this. It is a contact cement. Spray on both the carpet and wood and wait a few minutes, apply.
Birch veneer ply will stain nicely, then sand, hand rub a few coats of tung oil. Or there are other finishes you may use. It is also a good surface to apply other more exotic veneers.
A trick to "taping" the raw ply edges. Sand the edges so you have a nice, smooth edge. Paint on a coat of carpenter's glue (Wilhold, Elmer's) and let it soak in and dry. Most of it will soak in. Wipe away any drips with a damp cloth. After the first coat has dried, apply a second. While that is drying cut a piece of the birch tape (veneer 7/8" wide for use on 3/4" ply) a little longer than the piece to be covered. On a work surface, or old 2/4, tack it (I use push pins) on each end, glue side up, so that it does not curl up. Paint a coat of carpenter's glue on the tape. Use a 1/4" paint brush, don't let glue go over the edge and get on the "good side".
After both the birch tape and ply are dry, position the tape over the edge and IRON IT. I use an old household iron, like you use for ironing shirts. Turn it up to high, Cotton/Wool setting. You may also use one of the small irons made for veneer. Or go to a hobby shop and ask for a "monocote iron".
As you iron along the tape, it will melt the glue and will adhere. Follow behind the iron with a soft cloth and press down while the glue hardens. After it is all ironed down, use a utility knife with a NEW blade and run down both sides, trimming off the excess. A light sand with a sanding block and 220 paper will finish up nicely.
No drips, no runs, no errors!
Parts Express has all the hardware you will need, corner protectors, feet, handles, binding posts, terminal plates, etc.
For home stereo speakers 5 way binding posts are most convenient and troublefree. DO NOT USE spring clip terminal plates. Your terminal plate, regardless of type of connection (1/4" phone, posts, Speakon, etc) must be airtight. If you use 1/4" phone sockets you must use some sort of cup over the inside of the terminal with the wiring fed through and sealed.
I use E6000 or Aleene's Platinum Bond 7800 (both craft store items or Walmart craft dept) for gluing crossover parts, sealing around wires, etc. This is THE stuff to use.
Let's talk bracing. For a large speaker, run a 1x4 edgewise diagonally across the inside of the back. Glue it. Lots of glue. (I buy it by the gallons and refill smaller bottles use for application). Run another 1x4 edgwise across the inside of the baffle board just above the woofer hole, between the woofer and mid or tweeter. Finally, run another brace front baffle to back. For really large cabs, over 7 cft or so, you may need to brace the sides with a diagonal 1/4 as well. Generally if the width of the panel is under 12" it is not necessary.
I have glued crossover parts directly in the back of cabinets, reaching through the woofer hole to solder, but this is difficult. And if you need to modify the crossover later, very difficult. What I usually do is build the xover on a project board, with labeled leads. See this thread for example:
http://audiokarma.org/forums/showthread.php?t=65871
For small speakers I glue it with blobs of E6000 on the corners to the inside of the back panel near the terminal plate. For large speakers I glue and tywrap it to the 1x4 front to back brace just above the woofer. I then snake the leads out of the various holes so that I can solder the wires to the terminal plate, tweeter, woofer. When you screw in the terminal plate and drivers, be careful that you do not allow the wires to push up against the woofer cone.
Damping, I will no longer use fiberglass... I don't want to breath in the fibers, don't want it on me, don't want it all over the shop. I don't care how well it works in the speaker. I'll use other materials and do the best I can.
For ported boxes I use a 2" layer of dacron poly fiberfill on the back wall, held in with staples. On the sides and bottom I use carpet scraps cut roughly to shape leftover from covering other speakers.
For sealed boxes, I use an appropriate amount, sometimes even mostly filling the box, with poly fiberfill.
For really large boxes, even though home stereo use, you may want to install rollers and handles for moving around. Parts Express has some rollers that will inset into the bottom rear edge.
http://www.partsexpress.com/pe/showdetl.cfm?&DID=7&Partnumber=262-282
You make the speaker sit level by using rubber feet under the front corners. They also have, under the Dayton label, some handles that set into the upper rear edge.
http://www.partsexpress.com/pe/showdetl.cfm?&DID=7&Partnumber=262-820
Truck bed liner makes a good finish for pro audio gear. You can get a kit with a texture roller to give a pebbly finish. It is easy to repair, or touch up. A little Bondo, sand, and recoat. This is similar to the finish on Voice of the Theatre and other large speakers.