Lots of used ones out there on the forums for in your price range. It was an interesting hobby for a while.
Unlike places to deer hunt though...relics don't repopulate after you take one or two off the property. So the more stuff you find...the less stuff in the ground that there is to find in the future. Ultimately this is what got me out of the hobby. It took a while and lots of $ to realize that fact. I kept thinking I would find the magic detector and be able to go back to all my sites and they be like new again...when in reality, I was doing good to find maybe one bullet or piece of melted lead that I had missed. The key is researching new areas to hunt all the time...and being able to get on them. Unfortunately...most of the places have been built upon, previously hunted, or the land owners just don't want anybody on their place. If you think it's hard to find a place to deer hunt...you wait til you run out of family and buddies that own land and have to start knocking on strangers doors asking to metal detect. Stuff is still out there but to me, it got to the point it wasn't worth the hassle anymore.
If I were you, I would try to find a used Garrett AT Pro. New, they run about $550 but used, you should be able to get one at the upper end of your price range. That detector is a solid machine for the price that it costs. I've used them all the way up to $5,000 and everywhere in between...that AT Pro would hold its own against those twice the price of it.
Don't be so carried away with depth. Most of the stuff left in the ground ain't because its deep...it's because it's masked by iron. Some machines have a hard time hunting in heavy iron...like in Civil War camp sites and around old home sites or mill sites. They do a great job in open areas and such...but get them in square nails and things like that, and they will start to knock out the good stuff simply because of all the iron in the ground. What matters most these days is decent depth but exceptional target unmasking ability. The AT Pro is one of the best at it. The XP Deus is another one that excels in that area but it's way out of that price range.
Tesoro...I ain't fond of them at all in Tennessee or Virginia dirt WITH STOCK COIL configurations. To get them to really excel, you have to get after market DD coils, in which cost about $200 a piece. So your $300 machine now becomes a $500 machine just to get it to perform well here. When looking at them if you live in TN or GA or AL or VA...make sure it's got a DD coil on it. They handle our mineralization better than regular coils. Most detectors are coming stock with DD coils now anyway.