Can I have Multiple Internet connections at my house?

At the moment. I'm with slingshot on unlimited. I'm using our ex-ISPs modem (as the slingshot one has only 1 Ethernet port). I havea a 5m cable to one PC. And a 30m cable to another router in the garage where that cascades off to 4 more PC's a PS3 and yet wireless access point. (As the signal to the garage was kind of weak)

Everyone of my siblings has a iPhone or Android phone + an iPad, 2Laptops + 2 Notebooks (Yes we have a huge family lol)
They always use the internet. And I mean always. So just by that you can see that there's quite a bit of devices running off the one internet connection.

The problem I have is that when they are using the connection it makes my game laggy. Which usually leads me to disabling the Wi-Fi temporarily (until my game finishes) then that leads to my sisters yelling at me lol

The current speed of my network atm is 30mb down, 1.5 up (estimating as I'm not home as of yet)

Is it possible to get another internet connection put into my house?
I can give everyone the password to the current connection, and use the 2nd connection (yes will have to buy another 30m cable or whatever else) for myself and the other PC's in my garage.

Or is there a decent (Not too expensive) router I can purchase that has 4+ ethernet ports. A decent Wi-Fi. And settings where I can limit the traffic of the Wi-Fi. So if it does get laggy I could just throttle the speed instead of completely disabling it?

Added (1). Edit: oh yes sorry. It goes from my main router to a switch. Sorry (long day for me). And from that a switch to a wireless access point.

Thanks for that, also how much would that be? To install a 2nd phone line?
So it is possible?

First you are better to us the router provided as it will be compatible with your connection. If you want a second connection you will need a second telephone line or cable service. You should NEVER connect more than one router to the same provision as it slows it down. It can also cause conflicts which will make the system unstable. If you need more ports you should buy a network switch to connect to it. Then all other connections come from that including the access point.

First you are better to us the router provided as it will be compatible with your connection. If you want a second connection you will need a second telephone line or cable service. You should NEVER connect more than one router to the same provision as it slows it down.