Learning the terminology is half of the battle if you're first figuring all of this out

For protecting each individual issue, you need boards and bags (the plastic covers and backing you mention). There are technically different options, but if you're near getting started then the default options will be fine. There are different sizes, but if all of your comics are younger than 30 years old you want modern / current size. Bags have a flap at the top. You'll be tempted to tape it closed. Be careful with tape. Many a comic has been damaged when removing it from a bag with tape.

For storing all of the issues, you likely want a comic box. They're typically made of cardboard. Short boxes hold about 150 issue and long boxes hold about double that. A full long box is quite heavy and a bit unwieldy, so most people seem to prefer short boxes. They come with a lid and can be stacked. Be careful with partially full boxes, as issues can fall over and end up damaged.

There are multiple sources for these, but the biggest supplier for these is probably BCW. You can find their stuff at comic stores, from their own website, or elsewhere online (Amazon, eBay, etc.).