Finance, political and technology websites are some of the better places to write for, because those are popular niches. But you need to know your stuff so that you're a credible writer.
You mention that you want to start off at smaller blogs, but there's your problem right there. Most small blogs don't generate enough traffic and earn enough in ad revenue to hire writers. They're usually a one person operation and are probably earning a couple hundred dollars at best.
Small but more established blogs may be able to hire a couple of writers, but the pay rate will likely be very low. I've actually come across blog owners who want well-researched 1000 - 1500 word articles, and only willing to pay between $ 5 - 10. Now, I'm not going to knock these blog owners for paying so little. It is a free market after all, and writers may choose to write these articles to earn some extra cash.
Larger established blogs are still your best bet. You're likely to work in a more professional environment and get paid a more reasonable rate. It may be harder to get accepted but it's definitely worth your while to make the effort.