We have had luck contacting businesses that had no personal attachment to us or to racing in general. We contact them through email/social media and offer to bring a package down to them to look over and see what we can do for them. The biggest thing is to realize it is the racer's job to bring value to the deal. A sticker on the car is a must, but won't get you the sponsorship. Having the car at their ship is good, but depending on the business that also might not get you anywhere. you need to generate an on-line presence, web sites, social media, to help spread the word about the sponsor. you need to be at tracks in the sponsor's area, and you need to do your best to promote them wherever you are. We pass out samples and sponsor merchandise at the tracks, put the sponsor logo on all handouts (photos, swag), take the car to multiple shows in addition to the shows we do at teh sponsor location, promote sponsor events on multiple web sites and social media, give them photos, magnets, stickers, etc to pass out at their store and at the events they go to (i.e. trade shows) where the car might not be there.
The key is understand everythign you are capable of doing, and make sure all that is included in a formal, professional looking sponsor packet. Then, if they are interested in learning more, shine yourself up and get to their place of business or meet at a suitable location face to face. Present yourself like you are already on the clock repping for their company - be outgoing, engaging, and be ready to talk about the car, race team, how you can help their business, and why you think they are a good fit. For example, I have had 2 sponsors on the car for several years. One is a dog rescue out of Alabama, one is a small batch dog treat manufacturer here in NH. the local race series here is sponsored by a craft brewery based in NH. When a local store opened with a dog as a mascot and they specialized in micro-brew beers, I approached them showing how I could tie in the other sponsors and increase their visibility at the track AND through mutual contacts. They signed up for the next 2 years.
As far as $$$, I always say something is better than nothing. I charge more for the "good" areas on the car, and if the sponsor pays more I will do more for them (extra car shows, off-season promotions, etc). but the $$$ should not be where you start the conversation. Once they are hooked and want to go to the next level, tell them "I usually get $x for this area of the car, but I want to make this work for you and we can come up with a plan that fits your budget".