Connecting a NAS correctly...

AFP is deprecated. Eventually, Apple won't support reading or writing via that protocol, and you'll have to use SMB. For now, we're still using AFP with our NAS. Mostly because our main client likes using characters in their file names the Windows SMB format doesn't allow.

1. What feels clunky? It's a networked device, so it naturally has a network IP address.
2. Initially, you don't. Your router assigns it one automatically, just as it does with all of your other networked connections. With our Synology NAS, it came with a small utility to search the network for the NAS to let you know what IP address had been assigned to it.
3. Favorites isn't the place to connect to a server. That's for after you're already connected. From the desktop (Finder), press Command+K to call up the network connection dialogue. If you have no entries (likely not), press the Browse button. Select the NAS and enter the user name and password you gave yourself in the NAS' settings.
4. Adding the NAS to the login items is fine if you always want it to connect when you turn your Mac on. The NAS itself of course has to already by on and ready before you turn the Mac on. Since we don't use ours every day, we connect manually with Command+K. Otherwise, we'd get an error most times we turn our Macs on that the server couldn't be found.

There are no other methods. As mentioned under number 1, it's a networked device. You have to connect to it via an IP address, just like any other networked device. The main difference is, the router knows it's there when you turn the NAS on, but it's not (normally) going to mount itself for you.

I personally wouldn't try using a NAS for Time Machine. Most of them run on a version of Linux, though that itself shouldn't really make any difference. But there are a few issues trying to do this:

1. A server doesn't have separate partitions. When you create a new sharepoint, it's really just a folder the server treats as if it's an independent drive or partition, when in reality, all of the sharepoints are actually all using the entire available space of the drive at the same time.
2. That leads to this. A NAS typically won't return the correct drive format in use to the Mac. Since Linux is controlling it, the drive is usually neither HFS, HFS+, APFS, FAT32 or NTFS. The NAS has its own format and tells the connecting computer something else (via AFP or SMB). Windows computers and Macs think they're using a Windows drive (SMB) or a Mac drive (AFP), when they're really using neither. Ours reports the drive as HFS. Which is impossible since we have one 3 TB drive in the NAS now, and HFS can address drives no larger than 4 GB. It would also limit file sizes to a maximum of 2 GB. To at least make some sense, it should report the drive as HFS+, but it doesn't.
3. The point of all of that is Time Machine is probably confused. TM requires a drive to be case sensitive. But the NAS can't do that without changing the entire drive to case sensitive. Remember, a sharepoint is just a folder, not a separate area of the drive. It can't carve out just a section of the NAS as case sensitive. If you were able to control the NAS' drive format and chose APFS, then an SMB connection would be required to access it. AFP wouldn't work at all.

You should set up your router to reserve a single IP address for the NAS, then you never have to do any research. You'll have to do some research to figure out how to do that, but it should be a feature of every router on the market.

You can add mounted shares to the Sidebar, but if you click on it while the NAS is not available, there is a delay/freeze for a few seconds while it tries to sort it out.

You can do the same in your Login Items, but that will open a Finder window of the Share when you log in.

You can also create a folder full of Aliases that point the the desired Shares on the NAS. You could then put that folder in your Dock and select from the shares listed in the Grid/List/Fan when you click on the folder in the Dock.

Coming from a long time windows user, with them i'd just browse to network and it'll list every device on my network, I right click the one i want and say "map".

That's essentially what you're doing when you press Command+K. You're browsing the network for servers and choosing/mapping one to connect to. The last server you connected to will be listed in the pulldown menu, as seen here:

All you have to do to connect is Command+K to bring up this dialogue box and hit Enter, or click the Connect button.

For multiple servers, you can choose each one you've accessed from the drop down menu and click the + button to add them to the Favorites field. Then it's Command+K, and double click as many server names in that list as you want to connect.

I've never taken the time to learn how to add them to the login since I have no need to. But I know it can be done. I've freelanced in various large printing and advertising firms where their Macs automatically attach to their servers when the Mac is turned on.

If they in fact do show up on the Desktop, then create a new Folder maybe named Shares on/in the Desktop, drag all those Shares shown on the Desktop to that Folder, drag that Folder to the right side of the Dock between Applications & Trash, this should give you a popup menu to select from.:-)

Mount that Share once, then once the Globe Icon shows up on the Desktop, drag that Globe Icon to the right side of the Dock between Applications & Trash. You now have a Dynamic Mount, a quick click on the Icon in the Dock will connect you.

On the multiple Shortcuts...

Mount them all, when show up on the Desktop, then create a new Folder maybe named Shares on/in the Desktop, drag all those Shares shown on the Desktop to that Folder, (you can even rename them once there, if you wish), drag that Folder to the right side of the Dock between Applications & Trash, this should give you a popup menu to select from.:-)

To automount them, drag those Aliases to the Accounts Pref Pane's Login Items Window.

Depending on your network & router configurations, you may be able to use a DNS name to access your NAS, but you should definitely manually assign/reserve an IP address for the NAS as suggested by another user.

Without any special router configuration you can access network devices on the local subnet using the following address format which is fine for small simple home networks:

smb://<name-of-system>.local