I've been studying Tuttle for a while, but would like to try something else.

Any lists in particular you all would recommend?

Also, I feel like I'm learning a lot of characters, but I still find reading newspapers and things to be too difficult. Are there any practice texts out there that integrate with lists?

Don't know if your stats represent how many characters you've actually learned but you need a lot more than that.

To be comfortable reading a newspaper, you need a working knowledge of 2500-3000 characters and around 8,000-10,000 words. You can start reading at around 2,000 characters and 4,000 - 5,000 words but with the assistance of a dictionary.

There are many practice texts - try Integrated Chinese, BOYA Chinese, NPCR, among others.

You might want to try the Chinese Breeze series of books. There are some associated lists for the books already in Skritter. This way your new vocabulary will have more context for you and might be easier to learn.

What Kevin said + don't forget that knowing characters / words isn't everything. If you don't learn grammar, structure, pattern ect. as well you'll never be able to read (fluently).

If you just want to learn characters quickly any list roughly sorted by frequency will do (HSK, most standard texbooks, a lot of usermade lists tagged something like "most common characters", "most frequent characters" ...)
But personally i feel it's easier to study lists corresponding to other material your working with, be it a textbook, podcasts, texts you have to make lists yourself, wahtever.
If you are looking for reading and listening material (appropiate to your level!) you should checkout hackingchinese.com, they got a big database for free (and unfree) resources.

Since you are asking for lists in particular, here is what i studied with / study with now:
-HSK 1-3 (took a class at the same time as well, but since it was talking only i didn't create a list for that) to -take the test itself
-Mandarin Companion ebooks (graded readers with 300 unique characters, fits HSK 2-3 very well, has ready lists on skritter)
-A classic textbook (I use hanyu kouyu now, but really any decent book will do, many have ready lists on skritter)
-Podcasts from chineselearnonline (progressive lessons, ready list here, free for basic audio only)
+ if I find interesting study material that has no ready lists I just make lists with unknown words by myself.

Thank you all for taking the time to answer my questions and help me out. Andy, those lists look great, I'm going to give them a try. Much appreciated!