Router + Wi-Fi repeater
Answer:
I am familiar with TP-LINK Archer C8 router, it is a powerful router. As for RE200 and RE210 repeaters are also good models, dual-band. If the question is whether such a scheme will work, Archer C8/C9 router with a repeater, then of course everything will work. Whether these devices will be enough to cover the wi-fi network throughout your apartment, this I do not know. I have no idea what kind of apartment you have. Perhaps one router will be enough. By the way, you can first buy a router, install it, and then buy a repeater, if necessary.
And if the question is to buy a repeater, or another router, it is better to take a repeater. After all, the same Archer C20 has no repeater mode, only WDS. This mode is not very suitable for you. If you buy a router, which will be as a repeater, it is better to take ZyXEL, or ASUS. But there is no sense in this, if you can buy a special device, such as TP-LINK RE200.
Of course, for maximum speed and stability of the wireless network, it is better to put another router, for example Archer C20, and connect it to the first one by network cable. But it is clear that this possibility is not always available. It is not very desirable to lay cables around the apartment.