There are a lot of good machines to choose from in your price range. I would consider a waterproof detector as it will give you more places to hunt. But if you are not interested in water dogging, then the XP dues is a great choice for relic hunting. But you can quickly get tied up in expenses if you buy a high frequency coil for different hunting.
Like someone else mentioned, the Minelab Etrac is a great detector that provides a lot of target info. I have a CTX which is very similar to the Etrac but more expensive. It's my favorite detector. Plus it is waterproof which I like for the creeks and rivers. Both are heavy but the CTX is better balanced. If you are strictly relic hunting, there are better options as these two detectors are excellent coin machines.
Garrett AT max is a great coin and relic detector. It has an adjustable iron audio where as the AT pro doesn't. You may have to invest in a different coil for better depth. The AT series are waterproof as well.
Also the Minelab Equinox 800/600 is a nice coin and relic detector. These are very fast detectors and are light weight. The multi-frequency platform makes it a very capable detector. The 800 would be the better choice due to it's advanced settings. The Equinox are waterproof also.
A lot depends on how complex/simple you want in a detector. Both the Garrett AT and Minelab Equinox are pretty simple and quick to learn. There are other good choices in detectors as well and I am sure others will jump in with more suggestions.