I think your use of the word "pro" was kind of deceiving. I think we all want "pro" results, but it takes a lot of knowledge and quite a bit of high end equipment to get what most consider to be "pro" (far more than what I personally have in either category).
That said, if I were in your situation, I would probably look to pass on the Mackie and pick up a Soundcraft or Allen & Heath mixer. Both brands come highly regarded and are rather affordable.
I would also skip the tape recorder and look at
an Alesis HD24XR. They're 24 tracks, fairly inexpensive, and are considered to be the best (read: both best sounding and least problematic) hard disk recorder this side of RADAR. A tape machine, as much as it would be great to learn to use and maintain one (hell, I was looking at Otari MX5050s on eBay not too long ago because I would love to learn to use one), seems to be a bit more advanced given the experience you mentioned, but I won't be one to pass judgement, as I have no more knowledge of it than you do. Also, with Quantegy filing Chapter 11 recently, who knows when/if they will be making tape again, or who will step up to fill the void. Tape is also expected to raise dramatically in price, and already has begun to do so from what I've read. To go along with the HD24XR, I'd look at getting a modest PC running wave editing software (I personally would go with an older version of Cool Edit/Audition) and a firewire card for the PC and FirePort adapter for the HD24. That way you can import tracks in to the PC to do wav edits, comp vocal tracks, etc. You don't need a top of the line PC for that...even the P2 366 laptop I'm typing this on can run CEP well enough to do the trick.
You also need to be factoring monitoring and cueing systems if you plan on tracking more than one musician at a time. Search the "Other Equipment" forum here...there are a plethora of well-recommended monitoring solutions there. A lot of people on a budget also seem to like Behringer's PowerPlay headphone amps. Headphones, like monitors, are a personal preferance and can run from a 5-for-$100 deal on some cheap AKGs to $100 or more a pop for some MDR 7506s or HD280 Pros.
Don't forget about cabling everything up. Mic cables, TRS cables, cables to link your mixer to your recorder...it all adds up really fast. Look to at least double that amount if you decide to use outboard gear and hook it all up with a patchbay.
Speaking of outboard gear, you'll probably want at the very least a couple of channels of compression and maybe some multieffect units for reverbs or delays. It all depends on if you plan to mix in or out of "the box", but since you want to go with a tape machine I'm assuming you're looking to keep a computer out of the scene. For compressors, probably the most highly recommended budget compressor is the FMR Audio RNC. You can order a pair of them (each unit is cable of stereo, but not dual-mono, operation) in a rackmount case from Fletcher at Mercenary for just shy of $400, I believe. People also seem to like some dbx compressors, and even the Behringer Composers on non-crucial sources. As for a multieffect unit, many seem to support the TC Electronics M300. It has a couple of different configurations and a whole host of reverbs, along with some other effects like delay and compression. It also has a S/PDIF I/O if you ever decided to utilize that.
Last, but certainly not least, are the mics. With those, the sky's the limit, and it really needs to be tailored towards what you're recording. A solo rap act doesn't usually need a setup to mic a live drum kit, for example. You mentioned that you want to look at one big-name mic like a Neumann in the $1000 range. The only one in that range that comes to mind is the TLM103, which I believe is regarded as fair at best. A lot of folks seem to like the Soundelux U195 for that dollar amount as a showcase mic. You could go a different route and look at the AEA 84 ribbon mic also. Beyond that, your price range really doesn't allow you to get too far into the mic game. I would say maybe a SM57 or two, some Sennheiser e609s (I hear Guitar Center's markup on these is really high...see if you can talk them down), and some sort of dynamic tailored for low end (bass, kick drum, etc). I have an AT ATM25 and I like it. I prefer it to the Shure Beta 52 but thats just me. The AKG D112 is a really popular mic in this range, and the Audix D6 seems to be winning a lot of people over. You'll also want a pair of small diaphragm condensors. MXL, Oktava, and Studio Projects all make good budget SDCs that many people here use. If your budget allows, you could also look at a matched pair of Neumann KM184s or Josephson C42s...either of those will clock in at about a grand for the pair. Again, the mics should be tailored to what you'll be doing.
I hope this helps you out, but really all I told you is what I would do in your situation. Also, most of my recommendations are made based solely on the good word of many posters here that I trust and respect, as my personal setup is horribly modest. For what its worth...