Keep it simple folks...

Here's my go at explaining the same thing as everyone else:

Whatever else you do, you need to add a switch. Get one of the appropriate size for however many ethernet ports there are in your house (plus an extra port for the router). Plug it in next to the ONT and connect up ethernet to each of the rooms with patch cables.

You then need to choose whether you're going to use your Asus unit (which is a combo router/wireless AP) as a router or an AP. Whatever you don't choose, you will need to purchase.

If you use the Asus as a router, plug one port into the ONT and one port into the switch. Log into the router and disable the wireless AP function. You will then need to add a wireless AP. Something like a TP-Link EAP225 is good value. It's powered over ethernet so you don't need to use a power plug in the room where it is. It comes with an injector (alternately you can spend more money on a POE switch which will let you skip the injector). If your house is big you may want to add a second AP for better coverage.

If you use the Asus as a wireless AP, plug it into one of the ethernet jacks in one of the rooms of the house (as centrally as possible). Configure it to be a wireless AP only. You will need to add a router. TP-Link ER605 is a good cheap option and will route up to gigabit. Plug the router into the ONT and into the switch.

I would personally recommend using the Asus as a wireless AP, unless your house is very large. It'd be much more expensive to get a dedicated AP matching its wireless speeds than it would to get a dedicated router matching its routing speeds. Plus those spaceships look silly in network cabinets.

Others have mentioned other options which would involve purchasing less equipment. Mainly that's:

a) to keep using your Asus as both router and AP by connecting it to a double-run of ethernet - one going back to the ONT and one going back to the switch. As you said that has disadvantages because you don't have many suitable places in the house with double runs.

b) get a free router from your ISP and use that as a wired-only router in the garage and your Asus elsewhere in the house. This could work fine, depending on the router, and is probably worth trying first. Especially if you may not live in this house for a long time and want to minimise the amount of equipment you're purchasing that you might not need in future. If this is a long-term rental I'd be more inclined to spend the money on proper gear. Also as nztim said, if you don't need all the ethernet ports in the rest of the house to be hooked up, you could even get away without the switch and save more money.

everyone seems to have their own opinion on which AP is cheapest/best/ etc use what ever hardware your comfortable with but you will need more than what you got? 

Jase2985:

 

corksta:

 

You can have both. You'd place a switch in the cabinet in the garage connected to all the rooms that have Ethernet, then that would be connected to your router (via Ethernet) in whichever room that is in, then that would give you wireless and wired ports throughout your house.

 

 

no

 

router has to go before the switch,

 

Not necessarily, but this configuration would pretty much overwhelm the thread starter. Coffeebaron has said it all.