Forget analog. It's dead, and it will be increasingly difficult to find tape. The ONLY manufacturer of analog tape went belly up a couple of years ago, and it took a long time to get things going again.
The "rich, warm sound" is less an artifact of the technology and much more the result of the old trained-and-mentored engineer -- who usually WAS an engineer, not a high school dropout -- studio system. Engineers talk about how much they love analog mostly because it's what they know, not because it's inherently superior. Analog had a history of 100 years behind it, after all; when digital is that mature there'll be no comparison.
For a person who has not been through the old training process, it's at least as easy to screw up analog sound as it is digital, and fixing it is a hell of lot more work. I do a lot of digital recording and nobody has ever said "damn, that's no good! It sounds digital." Instead, they say, "how do you get that to sound so good?"
Go digital and devote yourself to making it sound good, not to some imaginary ideal. Concentrate on good mics and preamps instead of some old worn-out aging darlin' of a tape deck. Given the prices they command among the starry-eyed, if you got a multi-track deck and some mics, the budget would probably allow for a couple of Chinese $99 specials.The fact is that all that rich, warm analog gear is astronomical in price to acquire and maintain (and maintain and maintain -- every session) to give you potentially a marginal improvement in sound (along with a large increase in noise).
I started out with an 8-track reel-to-reel (this was, naturally, a few years ago), an analog 8-bus mixer, and hardware processors. When I got into digital, there was a steep learning curve, but now I'd never go back. I LIKE concentrating on the music and not on being the electronic technician on 24-hour call. I LIKE cutting and pasting with a mouse click instead of an Editall block and a razor blade.
I use the D888 for live and rehearsal recording and it's good. For critical recording you'll want decent preamps (I have an ART and a Grace) and, again, good mics. I also use a computer with Adobe Audition and a couple of Tascam digital mixers for recording.