Hi there
If you know of the nfcs.net site, there's a lot of singer-friendly information I put in the FAQ over there (much of it gleaned from discussions here and/or pointing to links which are "TS approved"
) Far from exhaustive, but hopefully helpful:
http://www.network54.com/Forum/174559/message/1127138105/What+is+the+best+recording+device+to+buy-+%28updated+Dec+2005%29http://www.network54.com/Forum/174559/message/1100702120/Recording+equipment+-+what+do+I+need-Bottom line is that for recording a big voice IMO and experience the mics are going to be the most important part of your set up. Fortunately, there are quite a few relatively reasonably-priced mics which cope well with operatic sounds (and it's easier for men than women, simply because you're in a lower frequency - regardless of volume, this is usually easier for mics to handle).
THAT SAID, I don't think you necessarily are going to need an $800 budget to start with. That would be ideal, but if you need to slim it down, it's do-able, particularly with Sound Professionals dropping the prices on a few of their AT-based mics. You can probably do what you're hoping for about $300-400 if you're willing to go 2ndhand or refurbished on the recorder itself (such as Minidisc or JB3).
Shoot me a private message via this site and I'm happy to help any further if I can - I am but a lowly n00b and bow at the feet of the Recording Gurus of this site, but I'm a professional opera singer and have really fallen in love with taping so have been learning a lot along the way.