Was chatting to a friend of mine about this and she recommended a bike no ones mentioned yet a Kawasaki ZZR600 - that should fall within budget and does have a low seat. Might be worth a look too?

If you are going the lowering route I'd certainly check it out before you buy the bike. You dont want to buy a bike then realise the options for lowering are too expensive.

I know many people here have lowered bikes without a problem but I'm not a fan. The bike manufacturers spend a huge amount on R&D when they design and build a bike and if you are changing something fundamental it must affect the bike. But hey I'm no expert all I know is that I could tell a difference in the two lowered bikes I've ridden but in fairness I've been riding bikes for many years and have owned and ridden quite a few.

Hope you find what you want.