I'd be careful burning either shingles or old tires -- in you live in a "environmental friendly" area. Often burning them is prohibited, and they give off a black, black smoke that is very visible and an odor that doesn't lie... Know what your local laws are before you start.
Even though I typically start a fire with paper, I've found a small pump sprayer (garden sprayer type) with a couple gallons of diesel or kerosene to be quite valuable in getting a good hot fire going. For example, if it is calm with no breeze, you can "lead" the fire to go all the way around the other side of the pile, by adjusting the nozzle and squirting a small stream (not a fine spray), then trace an unbroken path to where you want it to spread. The fire will safely follow the trail of fuel. I don't have a gas-powered blower (only electrical) and so i've had to find other ways to get a good, hot fire going.
CAUTION: Don't pump up a lot of pressure -- you want to just be able to squirt a small stream a few feet -- and make sure you've adjusted the nozzle to stream not spray.
Couple of other tips that have worked for me:
1. Don't put a dense mat of small stuff down on the ground. A fire must get plenty of air to burn. Instead, make sure there are lots of passages for air to get into the bottom of the pile. (Think the Boy Scount examples of "log cabins" or "teepees" made of fireword before starting the fire.) Instead, put the smaller stuff on the top of the pile. Then pile up your kindling (pitch pine or "fat pine" is the absolute best), paper, or whatever you're using in one concentrated spot and light it. Your objective is to get flames going large enough to reach up through the pile and catch the smaller stuff on fire that you placed on the top of the pile. Once that small stuff on top ignites, it will create a draft up through the pile, pulling the air into and up through the pile...
2. You can make excellent waterproof firestarting material by recycling the remains of old candles, parafin or sealing wax. Melt it, then soak strips of corrugated cardboard in the melted wax. Makes great fire-starters, burns hot, and is easliy lit, even when it is wet and damp outside -- the safest time to burning slash piles, as mentioned earlier...