I think as a general rule the all in one "studio in a box" is a better option for newbies - in particular if you anticipate that the majority of what you plan to record will be solo stuff recorded one track at a time.
As Kevin points out the all in ones can provide built in preamps, effects CD burning, etc with the ability to record numerous virtual tracks, etc. While most of these built in components may not be a good as dedicated rack gear, for most people they are more than enough.
Like any equipment purchase, you need to determine what you want to achieve and then purcahse the gear that meets that goal. If you plan to record live drums (vs. samples, loops whatever) you will need anywhere from 2 to 8 (or more) inputs. a 3 or 4 mic technique can work well, and some 2 mic techniques can also work - but with live drums I would suggest allowing for 8 inputs. If you plan to record other instruments at the same time as the drums you then may need 12 - 16 inputs.
You can spend from about $600, maybe a little less (8 tracks) to about $2500 or more (16 - 24 tracks). Plan on maybe $200-$400 for a decent condensor mic (for vocals) and maybe $200 - $400 for some dynamic mics (or a drum mic pac - which may even include 2 condensors for overheads).
I would think the Fantom should be good for most keyboard parts (and even drums parts). Another question you do need to ask yourself is what level of MIDI application do you plan to use? Most table top studios have limited MIDI capabilities (that's where the various computer based systems really come in. If MIDI is not a big deal, then a studio in a box is still likely to be your best option. If you pland to use a lot of MIDI then a computer would be better.
I would think most Alt music (guitar driven) would be fine on a studio in a box, but R&B can have so many little keyboard parts going on that MIDI then becomes more important.
Welcome to the world of recording - just understand once you start, the gear lust will consume you (look at the trhead on this site about how much money people have in gear). This is not a "hobby" for the faint of heart or thin of wallet.