Hi and welcome to POTN,
All good suggestions...
55-250 IS is the least expensive, and entry-level lens in pretty much every way but capable of taking decent shots. You can often get this lens in kit with various camera models.
The step up is the 70-300 IS. I don't have much experience with it, so can't really say much about it.
At the top end of your price range is the least expensive of the Canon 70-200... The f4 non-IS that ahendarman mentions... This is a solid, durable L-series, excellent image quality, resistant to dust, etc... a real workhorse. But I'm afraid you won't have budget remaining for a 1.4X. The Canon is good, but current Mk III is $500 US, Mk II might be found for a bit less. The more expensive Kenko model is also considered quite good. (Nite: Don't be tempted by 2X on the 70-200... they'll cost more image quality and also effect AF, disabling it completely if it's a Canon teleconverter.)
A longer tele zoom is usually quickest and easiest to shoot with. Canon 100-400 IS, Sigma 120-400, 150-500 and 50-500 are all possibilities... They cost more new than your budget, but perhaps you can find used.
With any of these lenses it's very useful to have image stabilization... But that can add cost. Some lenses listed above have it, but others don't. The three Sigmas are now available as OS lenses, but were originally sold without it. The 70-200 mentioned doesn't have IS, there's one that does but it is more expensive.
60D is a nice camera, but if it leaves you more money for lenses, you might consider T2i (550D) or T3i (600D).