The internet will work with the repeater, but if you like to play some online games, packet loss / ping pings will bother you a lot. I know this from my own experience, I have this configuration:
Router (TP-LINK TD-W8960N) + Repeater (TP-LINK TL-WA750RE)
The repeater is set to 70% of the router's range. Unfortunately, it works so that when pinging the router through cmd, the packet is lost from time to time, the ping jump up to 200 ms in a moment, the accumulation of 10-20 pings with a value of 100-400 ms after a while and this situation repeats endlessly. If you have the option, lay the twisted pair cable and place an additional Access Point. Repeater from an autopsy I DO NOT RECOMMEND.
From what I see, you write that you have two of the two available LAN ports occupied in the router, the solution - unplug one device from the LAN port, plug the cheapest Switch there and plug these two devices into this Switch.
In summary, it should look like this:
Switch plugged into the router's LAN1 port
Access Point plugged into the router's LAN2 port
Two devices plugged into the switch port, e.g. LAN2, LAN3.
Problem solved.