bill001g :
First you need ethernet cable to connect the remote AP. You can get dedicated AP if you want. Places like ubiquiti sell fairly inexpensive ones. You can also use pretty much any consumer router even if it does not have a actual AP function by cabling to the lan ports and disable dhcp.
The concept of channel selection on AP is pretty much dead. Worked ok when we used to use only 20mhz channels. 40mhz is commonly used on the 2.4g band and there is only 60mhz of bandwidth so you can not have 2 devices and not have overlap. On 5g it is a little better there is 170mhz but 802.1ac uses 80mhz so you can only have 2 non overlapping. Of course the newest tri-band routers have 2 5g radios so they use both the blocks. This also assume you have no neighbors that also want to use wifi. Pretty much you try you best but there is no good solution.
The same of different SSID is mostly a personal preference. I prefer different so I can force it to connect where I want. The same SSID in theory makes it possible to roam but the end devices are really stupid and stay connected to a weak signal far longer than they should. You many times have to manually drop it and force it to search to get it to use the closer one.
If you use different ssid's you will still have to manually force what ever device to acquire the other ssid. Either way it will be the same thing. I think he wants to simply extend his wireless network to work through the house. Most people don't roam around a lot in their house when they are doing things. No need to add difficulty to the whole thing. The good thing with a wireless extender is that it is simply a relay point for the router to reach farther. Same security key, same ssid, same channel, normally easy hand off from the extender to the router. Easiest solution without adding all that complexity.