Haha, got the upgrade bug already?
Well at least that's the beauty of mix n match rack gear, the sky's the limit.
Don't be afraid of stealing some dirt cheap 'broken' subs as well if the size seems good to you. If the actual speaker in one is intact and well specced, you can often salvage it to upgrade another unit, or examine the PCB and caps/fuse for repair.
For the 4306 and HDMI/TV audio setup you have a couple choices. First off, look up the factory reset procedure, probably best to always start there with a used AVR. Usually something simple like hold a particular button on power up.
Next, make sure you have an optical cable, and check your TV for an optical audio output port. Most do, though there are exceptions. This well let you go from source to TV, then TV to AVR via optical. You will have top image quality this way, and still excellent sound, though sometimes the extra channels are not compatible. Alternatively you can run source to HDMI 1, 2, or 3 input to AVR, then HDMI 'Monitor' to TV. Unless you have a 4K/HDR AVR though, this will give you the best surround mode, but limit your video to 1080p. Some aftermarket gadgets can help you split a signal, so you can send video to TV, and audio to the AVR from the same source. This gets very tricky with HDCP and ARC and is not nearly as straightforward as it sounds though.
I can't say for sure on what sub you should get, it can be total feast or famine in the used market, so who knows what is available. Using RCA splitters you can also easily run 2 or 3 subs off the same AVR as well. Sometimes I'll run a very highly responsive 8" or 10" unit at medium levels, and combo it with a 12" or 15" unit for some deeper punch on different levels. Adjusting the crossover to keep one out of the lowest Hz if it handles it less than perfectly is always an option. I'll send a pic of my crazy living room rig sometime soon.
Happy holidays!