I find that all that I need to do is change clothes when I get to work.
For the sweating issue, as above, slow down and dress appropriately. If you're just starting to bike, you probably will sweat a bit, so a shower / sink bath / baby wipes with a change of clothes will probably help.
You intend to change clothes when you arrive at work, correct? (If not, there are other options ...)
Assuming a fresh change of clothes when you arrive at work, you can just slide into the restroom and take a quick "birdbath", wiping down your body by the sink before you put on fresh clothes.
Other advice: Avoid synthetic clothing, as it retains the stink. Wool is best if its available to you as a clothing option.
Also: people assume it is perspiration that causes you to smell bad, but its mostly bacterial growth. As counter-intuitive as it may seem, your best bet may be to a take a shower before you leave home (wiping off the bacteria since you went to bed), then riding at a moderate pace to work. Save the race sprints for your trip back home!
All quoted for truth... as additional info, coupled with the shower before you leave, either use antiperspirant as opposed to deodorant, or even better(cheaper) yet use hand sanitizer! That will work better! Also to reiterate above, take it easy in the morning, and push yourself on the way home!
Also, I tend to keep a collection of clothes at the office, so I always change when I get there and I don't need to lug them around. I would also recommend making sure you get head/tail lights, a small pump, and keep a spare tube/tire levers and/or a patch kit in your bag.
Rain - I have two bright yellow rain jackets, one at home and one at work.. If I ride in and it's nice, when I ride home I can tuck my back and myself into my second rain-coat and wear it home. If it's raining for my ride into work, I wear waterproof pants along with my rain jacket. I also recently got a pair of waterproof, pre-curved cycling gloves as a present this christmas, but I spent two years riding without them. They are nice for when it's in the 35~55 degree rain, but I got along fine before.
Also, the first two weeks of riding sucked! Then my body adapted and they weren't to bad. That was all with a hybrid/mtn bike. Then due to construction, my trip changed from 5.5 miles each way to 8 miles each way, and it sucked for a bout two weeks, and then my body adjusted.
This past summer, I found a 1989 Raleigh Tri-lite at a yardsale for $45, and I doubled the value cost of it by sticking a frame mounted pump (to handle the new stem on the tires) and a set of lights.
Don't be afraid to have to many lights, bright reflective vests, etc. Any point where you are on the road with other drivers, it's good to be seen first, though it sounds like a good portion of your trip will be on a bike path, that rocks!
Good luck, I wish you the best! Cycling to work was one of the best things I'd done for myself! I tend to listen to technical podcasts while i'm riding, which I don't really get time to do otherwise!