The Akai 4000 is a stereo consumer-grade recorder. They're cheap and cheerful, but with two main hangups:
1. The main control system is driven by a cam shaft made of very brittle metal. If it's broken the machine will be unable to enter record or play mode and fixing it will be a very interesting challenge.
2. The 4000 doesn't have a speed switch. To change speed you have to put a little shim around the capstan which usually gets lost. The machine is only able to work at low speeds anyway.
Realistically, this is probably not the machine you're looking for. It's nice if you want to transfer recordings, or if you want a machine for casual listening (try and find the GX version with the glass heads, though). It can even be made to work as an echo unit, but it's definitely not a studio machine.
For what you're planning, a 4-track or 8-track deck is a better bet. A TASCAM 22-4, Model 34, a TEAC A3340 or something of that kind.
This does only give you four tracks, though. If you need more, you either have to start mixing the tracks together, or upgrading to an 8-track machine.
For 8-tracks, the TASCAM 388 is popular, other machines using 1/4" tape include the Fostex Model 80 and the R8. There are a number of machines using 1/2" tape (The TASCAM 38, 58 and TSR-8 spring to mind) but these are more expensive and have a higher running cost.
Note that even for a 4-track machine you will need some kind of mixer as well (only the 388 has a built-in mixer section).
Something like this would work reasonably well for an 8-track setup:
http://uk.yamaha.com/en/products/link/106344
...there is also an MG102, but it has a few too many stereo tracks for my liking.