If your business is blog-centric, you can get started for free with a hosted service such as one from WordPress. You can always move to your own Web host later when you outgrow it or are ready for more.
Get Logos and Design Work
Numerous Web sites, such as Logo Ease and LogoMaker, will design a free logo for you based on options you set via a Web interface. The quality varies, but generally you can get the logo for free for online use. The services make money if you want to download the logo in EPS format, which is more suitable for printing on T-shirts and coffee mugs. A Web search for "free logo" will turn up dozens of additional alternatives.
Another, possibly better, approach is to seek out an independent designer to work on your logo. If you don't need anything fancy, you can find someone to do the job for $50 or less through a simple Craigslist ad. The advantage is that you get to work with a live person (with genuine artistic skills) to create something unique for you rather than a cold, computer-generated logo.
As for Web design, you're unlikely to encounter someone who can create an original site for you for a fee within our $100 budget range. If you can't afford a real designer from the start, begin with a simple layout and customize it as you go--but try to avoid making incremental changes every day or week. When it's time to redesign, do all the work at once to avoid confusing and alienating your readers for a protracted time.