Generally speaking, you want the X axis to have the longest travel. There probably are some exceptions, but almost every machine out there using a moving table has the X axis the longest. There are, however, some gantry type machines where the gantry moves in the X and Z directions, and the table causes the material to move in the Y material. Such a table could handle quite long cuts.
In my opinion, for making picture framing stock, a shaper table would be much quicker and more economical than a cnc machine.
Always try for more Z axis than you think you need. You're going to have to be able to change bits, chucks, and collets, and they take more room than you think. The Sherline, for example, has 7" of Z travel, and many guys find it necessary to install a spacer under the column to increase the Z height.
Building a router is very commonly done, but the cost of the materials may surprise you. I find that my projects always come in well over my estimated budget.
There is a "plotter" type device called "Klic N Kut", which is essentially a small mill using a knife for a cutter. These are made for Arts and Crafts applications (think ladies decorating) but seem to be excellent for cutting out parts from balsa.
Don't know how close you are to any industrial areas, or how much room you have, but industry is rapidly changing from the old manual machine tools to the very advanced automated "machining centers". The result is that there are a large number of Bridgeport vertical mills (and clones) out there for sale, at very reasonable prices. I shopped for a couple of months before buying one, and there seemed to be a new one up for sale almost every day. If you buy an older cnc machine, expect to replace all the electronics. The older stuff is hard, and expensive, to maintain. The newer stuff works much better, and costs a lot less. The trick here is to find out where these used machines are advertised for sale, and be ready to pounce when you find the right machine.
There are a lot of low-priced controllers out there which only offer three axes. Many of them offer a fourth axis. If you think you will need to add a rotary table, by all means make sure you can add a fourth axis.
The controller software is already equipped to handle more axes. EMC2, for example, is ready for 9 axes. Mach3 handles 6 axes, which is still more that most people will ever need.
My advice is to buy something ready to run, or almost ready to run, and go with it now. After you've had it a year or so, you'll have a lot better understanding of how it works, and what your needs are. Then decide if you still need/want to build something yourself.