In shotguns - you often get what you pay for ....and you can't just look at a gun ...its in the internals, the steel, the quality of the parts, how they fit, etc ...that makes up a lot of cost. It isn't just fancy wood / or machine engraving - that makes up the cost ...although that is part of it ...
There are a lot of good pump guns on the market - Remington 870 Wingmaster and Browning BPS are 2 of the better ones ( selling in the $ 600 price range) ...the lower end of the 870's is the Express models...and there is Mossberg, etc ...Benelli Nova is another gun worth looking at. On a $ 300 budget, I think I'd stay with one of the Rem 870's.
O/U's cost a lot more to produce - if they're done right / and Browning and Beretta have set the market for a long time with solid guns for the money and long term durable ( 250,000 shells or more ).... but to get into that arena means an investment of $ 1,500 - $ 3,000 depending on the model. But Browning makes about 25 different models of their Citori O/U ...and some of them may fit you / some of them may not. I like the Citori's a lot - but only 3 or 4 models - fit me personally.
In Semi-auto world there are gas guns and Inertia guns. A lot of the gas guns will cost you from $ 800 - $2,000 and there are good guns from Beretta, Browning - Winchester basically the same now, and Remington - and Benelli on the Inertia gun side. There are other mfg's out there ...but they have very spotty reputations for the most part. There are pros and cons to gas or inertia / but at least look at them as you get into this hobby.
Heed OneOunce's advice - and stay away from the SXS's for now...
Be careful what you hear from gunstore sales guys ...many of them have little to no experience. Go to your local club ...talk to some of the shooters, see what they're shooting, and why they decided to buy and shoot that gun ...look for some good used guns on their boards....
I wouldn't be in a rush to buy a gun until you really know more about the various mfg's and models / see what fits you ...
There are a lot of guns being imported from Turkey these days ...and a lot of them look pretty good / but they are not holding up to reasonable target usage ( a few thousand shells a yr ) ...but you might get one of the 3 of 10 that are ok / or you might not ---its hard to tell. One company that is selling a lot of guns is Cabelas - a TriStar brand / priced right - and they come with a 5 yr warranty ...so if you're looking for a gun on a budget / give their offerings a look.