These are the Web Hosting companies that accept monthly payments:
Godaddy offers monthly payment options on their Economy ($5.99/month), Deluxe ($8.99/month) and Unlimited ($14.99/month) hosting plans. You can use this 50% off promo link to get a 50% off your first payment. On monthly payments that's 50% off of the first month, on longer term payments 50% of the full price.
New! 12 months of Economy Web Hosting for just $1/month.
Hostgator offers a monthly payment options on all three of their shared hosting plans: Hatchling Plan ($8.95/month), Baby Plan ($9.95/month) and Unlimited Plan ($14.95/month). The Hatchling plan supports only a single website, while the Baby plan allows hosting of multiple (unlimited) websites on a single account. You can get a first month of hosting for just 1 cent by using a coupon code 1cent or just use their default 20% discount code if you want to pay yearly.
DigitalOcean is one of the best VPS hosts. They have plans starting from $5/month for 20GB of SSD storage and 512MB of RAM. A Virtual Private Server doesn't come with a control panel, web builder, Wordpress or any other software you get with shared hosting. It is a lot harder to setup than a standard shared hosting. You have to install your own Linux distribution, setup the web server and any other software you need. This is only for advanced users.