#1 Silicone. It's soft, nonporous, absolutely bodysafe, can be sanitized, and is easy to clean/take care of. It does tend to attract hair and lint as well, but a quick run under water will wash most off, and a little bit of hair or lint getting inside your rectum is just fine as long as you don't have worm eggs around. Silicone is soft so you don't have to worry about aiming wrong and poking or brusing something inside, yet it is stiff enough to be stimulating. I'd also look for something with gentle bulge(s) and/or a curve.
I often "clean out" first with a small enema (water or isotonic saline! No odd chemicals in the butt please). I advise people to check things out first for themselves, though. Many people really don't need to, a ordinary trip to the toilet gets things pretty clean for them provided they watch their timing and diet. I, on the other hand, tend to have an uncooperative digestion and/or am not good enough at watching my diet. I know I'm not good at "putting things off until a better time" either - if there's time and interest then I'll take her up on it. I find personally that things seem a little slicker when I have used an enema first. I hypothesize that the water dilutes the mucus in the rectum, and that serves as an additional lube as well as not scavenging as much water out of the add-in lube.
Do try getting a small oral syringe or similar to squirt a bit of lube inside - this can help things slide better. Sometimes people find that the anus "squeegees" off the lube if it's just put on the outside and you feel more friction.
Plugs stay in one place. Properly chosen they stay near the prostate and stimulate it and the rectum with little bumps as you move around. Probes or dildos are great for active play, because you can grab them and really give your or your partner's butt a good working over, whereas the shape of a plug can make "active" use difficult. Plugs are great for warm-ups, as a first course, or if you're doing other sexual activities, but if anal (on me) is the main course I often switch over to a thrusting toy in the middle of play.
Buttplugs, anal plugs, or just "plugs" are generally shorter toys that are bulged to stay in place without being held (some are more successful at this than others). They stimluate the inside of the anus, rectum, and prostate by their volume and wiggling.
Probes and dildos are very similar. Usually probes are all non-realistic and have a defined handle. Many times they are also either long and thin or in ridiculously large sizes. For the most part they overlap dildos in use. Dildos often have a base instead of a handle, for anal dildos it's best to look for a flared base so you don't have to worry about the toy slipping all the way in (you will usually have a firm grip on a probe). Some dildos are highly realistic, some are slightly realistic, and some are abstract. Some have various mechanisms that allow you to attach them to a harness (either the flared base or one of several patent mechanisms - stick with the flared base and O-ring harnesses whenever possible). I guess the short answer is that these are pretty much interchangeable, so call the toy whatever you like best.
