If you're tarantula is an adult its probably easier to use superworms so that it fills them up. Usually I'll try feeding superworms to tarantulas 2"+, though I've had ones as small as about 1" still manage to eat them live. Some of my adults on the other hand seem to prefer crickets so I'll feed those to them, not all specimens are the same.
Crickets are just fine and tend to get the very best feeding response from the commercially available feeders (red runners are right there with crickets)....If one has a picky t like teal mentioned, crickets are almost always the best.
IME very few ts will be picky though.....I mean I have several hundred in my room, and exactly 3 picky ones....My G. porteri, Thrixopelma sp. black and the runt of a G. pulchripes sac from a couple years ago....All 3 show a very strong preference for crickets. But that's 3....like less than 1.5% of my ts.....sooooo....picky is the exception to the rule.
Changing it up with regards to feeding isn't necessary though, but most of us do tend to switch things up every now and again, because why not....if nothing else, I like watching them eat different things. I do find fattier prey like meal or wax worms do seem to plump slings fast and I do see the fastest growth rates with slings fed almost exclusively on them...I also see a markedly better success rate with the success of sacs dropped by females fed primarily fatty worms (I have by far my lowest success with females fed exclusively dubia for some reason).
Now if you can cultivate moths, from hornworms or wax worms, I will say they get an "oh my god" response" pretty much universally among all ts.....something about beating .wings that just makes them seem almost excited. Picky ts WILL eat things with wings...provided you can get a safe supply of such feeders.
All tarantulas will take mealworms, all mine do with no problems. I don't buy the whole 'my tarantula doesn't like x prey item', in the wild they can't afford to be picky. If it doesn't take mealworms at first, put it on a 'fast' and then keep on trying, it'll take it sooner than later. No tarantula will 'starve' because it's too picky (unless the food item is too large then maybe).