A flat tire is just something that happens. If you have a lot of them, it might mean you need new tires. I went 2 years without a flat--and then got 2 less than week apart, one in front & one in back. I think my tires have some miles left in them, but I'll probably replace them next fall with kevlar lined tires.
My commute is 2 miles. I agree on fenders. Not only do they keep stuff off of you, they keep stuff off your bike, prolonging the life of your chain & drivetrain. Any day your bike gets wet, wipe down the chain when you get home. It might seem like a chore at the end of a long day, but it only takes a few minutes, and it'll prevent rust. If you do notice rust the next day, oil your chain and get that rust cleaned off. I got 4500 miles out of my cassette by keeping my chain clean & replacing it every 1500 miles.
A few years ago I invested in expensive goretex rain gear. It is waterproof and breathable, so I don't sweat as much in it. But I learned it is most valuable as an outer shell on the coldest days. In general, whether it's raining, cold, or hot, I wear an old t-shirt and bring a nice shirt to change in to at work. Only on perfectly nice slightly cool days do I bike in my work shirt (slowly, so as not to get it sweaty). Or if I'm not going to see any humans that day, only rats. The rats don't mind if I'm sweaty.
I find obstacles themselves to be motivating. I like to bike when the weather is horrible, and when it starts to turn nice I find myself in the car a lot. So I'm not sure what to tell you about finding the motivation to bike when it is raining, if you're not naturally contrary!
2009 Trek 7.2FX WSD, brooks Champion Flyer S, commuter bike