With new altcoins coming out every day, I'm having a hard time discerning which ones to take seriously, and which to disregard.

What criteria do you look for in a new coin that makes it stand out? Please don't spam me with a sales pitch for your coin. I would like to know the process for picking out promising new coins before they've already succeeded.
Depends on your what you are looking to do.
If you are only trying to make a quick buck,
Then Watch the
https://bitcointalk.org/index.php?board=159.0Try to get a few bucks in to a coin that has just gotten on an exchange within a day or so , and buy up a few bucks of it and sell immediately once it reaches a profit .
That way you profit off of the hype from its first exposure but don't hang around for the decline.
(That is what I see alot of guys doing)
If you are looking to have crypto take care of you financially in the Future.
Look into Proof of Stake coins with solid communities that have passed the 1 year mark.
This may take a few years and requires much more Patience & Commitment than the 1st choice, but as with anything the more time put into it the better the result.

Also never put all of your eggs in 1 basket, Diversify your Holdings and never sink in more than you can afford to lose, so small setbacks don't completely wipe you out of the markets. Small setbacks happen , especially to Newbies , so learn from them , so your future choices better reach your goals.