New Modem (no idea what to look for)

So, First off I live in Australia, so i don't have the best speeds.

But I've been using the modem i first got my internet a few years ago, and i feel like it's not really up to standards, lately it's been dropping out every now and then, especially when a lot of things are connected,

So i was just wondering what i should look for, and if I should do anything in particular that would help me get faster speeds or stop it from dropping out.

Are you "dropping out" as in disconnecting and is this on wired or wireless. Also, is your modem and router two seperate pieces of hardware or are they an all in one type deal?