I wanna try battling on this site, but since I was gone for SUCH a long time, I have no idea what to use with all these weapons out.

What would you feel is good for a Tier 1 pet to fight with?

And what are the stat priorities? Should I just do speed and attack like a lot of other sites or do they all actually matter?

This post has some good T1 options :D To be honest, T1 is very basic so you could use any T1 weapons you want. However, is one item you will use forever so it is a great idea to invest in it as soon as possible.

For stats, most people give priority to health and strength. Here is an explanation of stats and their functions.