I want to get lip fillers and get my lips tattooed as well. What do you recommend I do first?

Nebra223. I would recommend conservative lip augmentation with Hyaluronic Acid, like Juvederm Ultra plus to see if you like the look. Since both the lip and lip line are filled, it is best to have the lips tattooed first.  Another option is fat transfer which is more permanent. It is done under local anesthesia and fat is usually taken from the lower abdomen or thighs. Studies show that at least 1/3 of transferred fat last forever. Seek out a board certified plastic surgeon in your area, Good Luck!

It may be easier to identify the normal anatomic boundaries of your lips before filler, but I don't think it really matters either way. Filler placement really depends on what your goals are. Usually filler is placed just beneath the red portion of your lip. It can also be used to improve the "cupids bow" area of your lip and the dimple in the lip between your nose and lip (philtrum). Warm regards.

Hello Nebra223 
A photo of you lips would have been really helpful for my plan. That said, it always makes sense to have lip filler before tattooing.
Once you have the volume that you desire, a skilled permanent make-up artist can then work with this fullness to define the border and can sometimes even correct the appearance of asymmetry. 
That said, know that you will need to have annual touch ups to keep the color of the tattoo ink natural looking, and having tattoos in this area may interfere with future laser treatments if they are needed.
As for the second question "what actually being filled, the lip line or the inner part of the lips?" 
It depends on your natural lips. I sometimes float filler along the lip line and just under the thin mucosa. This gives a nice improvement in definition of the lips and produces subtle volume improvement without that "ducky" look that is  not attractive.  If the lips are very thin, then some volume can be added to the inner part of the lips. 
Hope this helps. 

You can definitely have your lips augmented with the new hyaluronic acid fillers that are available on the market, since these are after all temporary even though some of them are long lasting. I would discourage you from having a tattoo though, since that is something that is permanent and as you get older you may regret it completely and have a hard time removing it. Good luck from New York City