Yes - get yourself in an E39 and don't look back!

Best car ever.
Good advice from Fox and the others. 2k can get you a nice earlier SE no problem. But, imho, since all E39s are so cheap it's worth considering the whole spectrum of the market and seeing where you want to be if you are not necessarily limited to 2k.
For example, only 1k more is in the region of tidy late model facelift sports. E.g. this one...
http://forum.bmw5.co.uk/topic/89576-2002-bmw-e39-530i-msport-auto-grey-18-m-parallel-staggered-fk-auto-coilovers-leathers-sat-nav-updated-add/
Slightly high mileage but tidy looking and a great spec. You may not fancy the modifications, but it's just an example.
Then around 4k plus, you are looking at truly special Individual models, amazing spec, low miles, low owners etc...
http://forum.bmw5.co.uk/topic/89276-2003-e39-530i-m-sport-individual-60000-miles/
And that's pretty much the price range of the entire market of good examples (not including M5) - about 2-2.5 k from top to bottom. So as I said worth considering what you really want. If you would be happy with an earlier SE then absolutely fine - there's a certain appeal to an untouched immaculate original pre-facelift SE. If you'd really prefer a facelift sport with higher spec and/or you think you'd spend money upgrading/retrofitting if you started with an older car, then you may as well start with what you really want in the first place.
I'm a sucker for high/rare spec so mid-2012 I went in at 4k which got me a 2001 facelift sport with crazy spec (even double glazing!), and only 2 owners, 55,000 miles, FSH etc etc. That hasn't stopped me becoming hopelessly addicted to upgrading and retrofitting even more options (and stuff that wasn't an option). My latest ebay purchases should have me certified

. But I'm loving it - it's such a great car.
Get yourself on BMW5.co.uk too.