So, if I add a rack to the back of the bike (Trek Soho) will it dramatically alter the way the bike responds through the many twists and turns in the path system I ride?
A bike with a rack and loaded panniers will ride more or less the same. The only time the handling is different is when you are not on the bike and are walking it about, and this is a rather marginal case. When I ride with 30# of stuff in my panniers, the only difference I can detect is that my bike has more inertia (which one would expect) and takes longer to stop and accelerate. No different from hauling 30# in a backpack, at least.
Which do you think will give me the most efficiency, continuing with the backpack, or switching to a rack or pans?
I'd switch to a rack and panniers if comfort becomes a very large issue for you (and it sounds like this might be the case), or if you're interested in hauling more than your backpack currently can move. A rack with panniers can comfortably move more volume and more weight than a backpack.
I used to use a backpack (messenger bag, actually) to haul about a 10# load to and from work, now I use a rack and panniers. I prefer the rack and panniers for reasons of comfort, mainly. It's nice to ride around in the hot summer without anything on my back. It's also nice to be able to haul a week's worth of groceries in a single trip, which I couldn't do with my backpack.
If you go the pannier route, you might want to look for a pannier bag that has a fold-out shoulder strap. Then, your pannier bag can magically turn into a shoulder bag/backpack and vice versa. Very handy.