The advantage of a drop-away rest is that is creates very little contact with the arrow, which makes it more accurate than the brush-type (whisker biscuit, octane hostage, etc.) rest, and it's less likely to be hindered by bad shooting form because of its minimized contact with the arrow. Having said that, I used a whisker biscuit rest for a number of years because I liked that it fully contained the arrow, and I didn't have to worry about it falling off and such, but my accuracy improved quite a bit when I switched to a drop-away rest.
I use the Ripcord Code Red rest, and I've been very satisfied with it. It is a full-containment rest, and you'd have to be pretty careless to have an arrow fall out of it. I have it mounted on a Bowtech Experience, and it is very accurate out to 80 yards with fixed-blade broadheads. If I were getting a drop-away today, it would be the Ripcord Ace because the Code Red version that I have lowers when you let down, but the Ace does not. It doesn't happen very often in a hunting situation where you have to let down, but I think there is a definite advantage to being able to let down without worrying that your arrow is going to fall off and make a racket. I've heard good things about the QAD rest as well, but I kind of like the fact that I can reset the Ripcord rest with the thumb of my bow hand rather than having to reach around with my release hand to reset the rest (like is the case with the QAD rest). I think it makes the process a little faster and creates a smaller amount of movement if you do get a second shot.
I don't know what type of rest you've got on your bow now, but I'd probably shoot it some and see if it gives you decent accuracy at your desired distances before you go and switch to something else, but I think you will find that you get a fair amount more accuracy from a drop-away.
Good luck, and enjoy. Archery is a blast. I don't know that there's any more gratifying way to fill your freezer.