The Cricut Explore Air (newest version) can be found on sale this time of year for about $250 (I just paid $229 for it as a bundle with extra stuff from JoAnn's Fabrics for my wife). Maximum material cutting depth is 1.5mm so 1/16th balsa is barely doable if it will work (testing required). Cricuts don't actually print they either cut with a blade cartridge or draw using special ink pens. Multi-piece vinyl decals are doable, they just take a little extra work lining the pieces up on the transfer tape. The mats that the Cricuts uses are expendable in that they have an adhesive on them to hold the work piece being cut, they come in 6"x12", 12"x12", and 12"x24" (there may be others). If some already owns a cartridge with special designs from an earlier model Cricut they can still be used via the online software, you just enter the cartridge serial number into your accounts database.
The Explore has several variants the main ones being:
Explore Air= Bluetooth built in and two cutter/pen holders so it can cut or draw,
Explore=USB connection to computer or a separate bluetooth adapter is available for purchase, it also has 2 cutter/pen holders,
Explore One= USB connection, not sure if Bluetooth adapter is available but probably, ONE cutter holder or pen holder.
Edit: iirc all the models can do the same functions other than cutting and drawing without changing tools, the Explore One only having one tool holder requires changing tools before doing another task, where as the other two model can cut then immediately start a draw operation without changing tools.
The Cricuts are really neat tools but they do have a fair learning curve, I happen to have 3 sisters, 2 sister-in-laws, and my Mother that all own them and most of the cartridges between them, the new cricut can make use of jpgs and other file formats in the Design Room online software to create your own designs. Maximum size of work piece is the size of the largest mat iirc so about 12"x24". There are probably lots of things I have missed but basically if its under a 1/16th of an inch and you can cut it easily with a Xacto knife then the Cricut is able to cut it, as for the thin aluminum its probably more like foil thickness. My wife is just itching to get at her's, of course I plan on using it as much or more than her.