theres nothing easier, and possibly cheaper than recording on a computer that you already have (given it has a soundcard; decent specs..and you have a limited knowledge of using a computer). it depends on what kind of quality your looking for. im not really sure what a 'boss 900' or 1600 is, ill assume its a disk recorder. iv only used a few but i wasn't to fond of them. i would prefer a 4-track tape over one of those 7 out of 8 days a week. but if your looking to go the computer rout your going to have to get a fiew things.
Interface: something that 'takes' your audio to your computer. you can usually get a small mixer, (and for what your doing youll only need a few tracks) for about 70-100 dollars. or you can get some sort of usb or firewire interface. presonus makes a decent one for about 200 bucks.
software: theres a huge variety of sequincers that you can choose from. if you want to spend some extra money and get something great, you can get something like Sonar 6 PE, or Cubase. if your down on cash theres some pretty basic but decent free ones out there. audacity is (dont quote me

) a pretty good starting point, to see if you really want to get into computer based recording. theres no reason to spend money if your not going to enjoy it, or if your alternative route( the boss 900 or 1600) would be better for you.
i enjoy doing computer based recording, theres almost unlimited possibilities when using a sequincer(computer based mulit-track recording software). but some people would prefere the most basic 4-track cassette recording, thats cool too its really up to you what you want but for beginners you could just start with the bassics.
your signal chain
might look something like this if using a DAW:
insturment--->mic/line---->mixer---->soundcard--->software--->moniters
---------------------------interface if no mixer----^
just for an idea of what everything is going to do.
good luck
-Matt
ooh btw dont forget to add to your list: your backing tracks
