I just recently got to the part in the Story mode where I can feed Pete items to raise her level, but everything I give her she doesn't like, and it takes forever to get the stats raised up. Is it supposed to be that slow? If so, it's going to take forever to get her to level 30 so that she can fight with me. What are the best items to give your Partner Machine?

That would depend on the type you would want. Since theres 5 diffrent kinds. the four "Pure" Partner Machines are idealy better then then 6th brand.

So what kind are you looking for? the Armor Pm that uses techs? The striking Pm that uses Melee weapons? The gun PM that uses guns?

Yeah, I realized that there were way too many different options to choose from, and therefore not deciding what I wanted beforehand was fruitless. Anyway, I found a guide for raising particular machines, and found out that it's supposed to be slow going unless you have a ton of money.