What I do is rinse the bottles out after I have finished the beer that was in them. Or at least I usually do that. Well for the first few beers of a session anyway.
Then before I bottle, I soak the bottles in Oxyclean/hotwater in the sink and rinse with hot water. Oxyclean is a cleaner, not a sanitizer. Well not an official FDA approved sanitizer, but that is a discussion for another time.
I have sanitized in three ways, the first is to soak the bottles in an iodophor solution after the Oxyclean soak, invert them in the dishwasher rack without rinsing and then bottle.
I have also used the oven, 350F for an hour, but they take a long time to cool, and my oven only holds about 48 bottles, so I am worried that I will be short bottles, even though I never am. But don't use this method if you want to bottle right after sanitizing, it will take hours for the bottles to cool. NO rinsing required with this method.
The last time I bottled, I cleaned the bottles in oxyclean, then rinsed. I mixed up some iodophor solution in a quart squirt bottle. I took the clean and rinsed bottles, squirted the iodophor solution in them from as many angles as I could, then inverted the bottles on the dishwasher rack to drain. Then quickly bottled. This appears to work well. A poor man's Vinator as it were.
Some sanitizers are contract sanitizers, iodophor is one; so when you rinse it, you have also rinsed off the sanitation.
I don't rinse as we have well water that is not treated. Still, I suspect that if it doesn't make us sick, it won't make the beer sick.
I prime the bottling bucket with 3/4 cup corn sugar dissolved in about 2 cups of very hot water, heated up in a microwave. I pour the priming solution into the bottling bucket, then siphon the beer from the fermenter to the bottling bucket which ensures that the priming sugar is well mixed. Also siphoning from the fermenter to the bottling bucket helps avoid getting the trub in the bottles in case you don't keep the end of the siphon tube far enough above the bottom of the fermenter. You get two chances to keep it out. The siphoning also stirs up the yeast a bit so they will be more active in the bottle to carbonate the beer. Or so the theory goes.
Soak the caps in sanitizer. Bottle and cap. This is best done with two people. I write the brewing date, the bottling date and some indication of the beer name on the cap with a very fine point Sharpie. So my Australian Sparkling Ale cap would read:
ASA
12/27/9
1/28/10
on the cap, It is also worth bottling one or more in a clear plastic soda or sparkling water bottle. Just clean and sanitize the bottle and bottle cap, then screw it back on. This way you can tell how carbonation is progressing by squeezing it; when fully carbed it will be very hard, how it is clearing, and how the yeast is depositing out. If you keep the clear plastic bottle out of sunlight it will not oxidize.
I also came to the realization that it doesn't matter if I get all the label off or all the glue off the bottle. I know it isn't what the label says it is. That is what the writing on the cap is for. If I pour from the bottle to a glass, the aesthetics of the served beer aren't affected.
If you find someone to help you that actually likes bottling, be very nice to them.