January is great in terms of crowds... or lack of crowds. The first few days are crowded but once the New Year's crowds leave the rest of the month is great. The marathon brings people in, but from what I've read the parks are still uncrowded, you just need to work around the runners and what parks they'll be going through, be wary of closed roads, etc, but that's only for the weekend. MLK weekend also brings in crowds, but again, it's really only for a few days then they taper off again. We've gone the last week of January several times and it's very nice and very uncrowded. This year we arrive over MLK weekend though.
As far as weather goes, it's variable... very variable, LOL. We've had days where we went to Blizzard Beach and days where we wore mittens all in the same week. Most days are pleasant for park touring but you do need to be prepared for hot days and cold nights both. Layers of clothing work well, IMO, because it's usually cool in the mornings and evenings but warms up nicely by midday.
Special events... New Year's eve celebrations, the Marathon, and the last two years there were Pirate and Princess Parties, though it doesn't look like they're having it in January next year, darn it.
There have been deals in January for as long as I've been checking. The last few years it's been discounted packages rather than discounted room-only rates.
As for which resort is best, it's a matter of opinion, I think. My favorite is Animal Kingdom Lodge, followed by Port Orleans (Riverside and French Quarter are both great). The only value resort I've stayed at is Pop Century. It's brightly decorated and clean with a great selection in the food court and doesn't share buses with any other resort and has only one bus stop itself. There isn't any resort I've stayed at that I disliked though.
Still on my to-stay list is the Polynesian. Up to now it's been beyond my budget. It's in such a convenient location, as are the Contemporary and Grand Floridian.