It depends.
How familiar are you with online MTTs? Are you familiar with multi-tabling online MTTs? Are you willing to grind them out?
If you follow the 100x buy-in rule for an MTT BR, $1K means you can start playing $10 MTTs, but it doesn't necessarily mean you should start there. Especially if you have no experience playing MTTs.
If you're just starting with MTTs, I suggest starting with the lower $1-$2 MTTs. Yes, it might sound crazy having 450-900x the buy-in (if we're including rake) for MTTs, but look at it as a stepping stone. MTTs have the most variance out of any game and you're probably going to lose a lot learning and understanding them, but sometimes that's what it takes to build a solid understanding and foundation for you to be able to beat them profitably.
Sometimes, players will just be naturally good and they can jump from one level to the next easily. For most, myself included, playing MTTs mean losing a lot before becoming profitable. And I'm not talking about losing because we get unlucky, but because we fully don't understand MTTs. Chances are you'll all into the latter category. Not trying to be mean, it just how it is.
So, starting off low allows you to have a bit of trial and error as you learn your way through MTTs. It's a lot easier to stomach losing 50-60 $1 MTTs in a row as you're learning than it is to lose 50-60 $10 MTTs.
Of course, this is only if you don't want to have to constantly reload the BR. Again, that is coming from experience but I was foolish enough to do that when I started playing. But, if you don't have a problem and/or have deep pockets full of cash, do what you want.
Oh, and whoever said to play 1-5% of your BR for MTTs, you really think someone with a $1K BR should play $50 buy-in games and they're just starting with MTTs?
lol