"The local providers want to charge me every month for their equipment when I would like to just buy it once. Also, I would like to know what type of internet service is available without going through TWC or ATT or the other large providers. I can't remember the term, but purchasing my own internet access at a lower monthly rate than the providers. Thanks."
It all depends, what type of service you are looking to purchase. Top choices would be FTTH (Fiber To The Home), DSL (Internet through POTs line), or Cable (Cable Provider). Centurytel and Verizon FIOS offer FTTH, and up to 1Gbps speeds, Comcast, TWC, Cox, and Charter are cable providers, and provide excellent service in my opinion. D3.1 will be rolling out 1Gbps speeds as well in the near future. FTTH is nice however if the plant is not prebuilt, meaning service provider has not built to you neighborhood, then that can get really pricey. DSL and Cable have been around for a while,and the technology is common, so the ability to buy an all in one modem/gateway is easy and cheap to find. If going with a cable company the standard going forward is DOCSIS 3.1, so just do a search on your favorite tech site will result in an abundant amount of hits for products.
Cable Modems:
Amazon.com: docsis 3.1 - Networking Products / Computers & Accessories: Electronics
DSL Modems:
Amazon.com: DSL Modems
FTTH:
Most of the EPON/GPON (Ethernet Passive Optical Network/Gigabit Passive Optical Network) devices are really expensive, you will most likely go with what the service provider installs, and that would be a monthly charge.
This day and age really any service provider will work, however for reliability I've never had any issues with Cable Providers. I know i might catch flack about that, however I also know that services can go out from time to time. It's up to the person to understand how all this tech works together, cause you can lead a horse to water, but you can't make it drink.
Hope this helps
eequalsmcsquared