1. Alder will be lighter than mahogany, so if weight is important, Alder might be better - LPs can feel rather heavy when your back is old and you're stood on a stage for a couple of hours.
2. Mahogany is a more typical LP wood, so if sound/tone authenticity is important, the Mahogany option is likely to give you a better "LP sound", particularly when you add in ...
3. A maple neck would give a harder/brighter edge to the sound than the warmer Mahogany, so again the Mahogany option should be a truer representation of the LP sound.
LP p'ups tend to be pretty standard in terms of size (don't often find LPs with wide-spaced bridge units or 7-string versions, etc), so you have a pretty full choice of BKP replacements - ie any standard HB size.
(that's a great linky to the Warmoth site too - I hadn't seen that before).