It depends on whether you have the intention to upgrade in the
future.
When I first took my 2b licence, I was already aiming for class 2
bikes, so I bought my first bike which is a second hand which total
about $1600 (RG125) for me to last about a year plus before I take
class 2A which I also used about $1600 (GSXR400-Old mother hen)
before I switched to a class 2.
All amount stated are OTR prices cos I didn't wanna spend too much
since I already plan to upgrade.
I know of people who are very happy with their 2B bikes because
it's low maintenance, low petrol consumption and easy to squeeze
through traffic. Upgrading never cross their mind.
Oh well, it all depends on you. $2000 is definitely enough to get
your hands on a second hand bike with relatively good condition but
you'll require some patience to get the best deal. If in doubt,
bring an experience friend along to view the bike.