If you are going to be riding some trails, a suspension fork might be right for you. However, good suspension forks are simply not available on inexpensive bikes. You may want to try to find a bike where the suspension can be "locked". This means you can sort of turn the suspension off or adjust the fork to make it more rigid as needed. But again, these type of forks cost $$$.
Regarding price...here is what I try to explain to my non-cycling friends who are shopping for a bike or want to start cycling. When I was a kid in the late 70s I really wanted a Schwinn scrambler. Scramblers were a decent quality, basic BMX style bike suitable for a kid. The price on those at the time was $200. As I recall, that was pretty typical for a reasonable quality LBS bicycle. Now, fast forward 35 years to today. Accounting for inflation, what would $200 in 1978 be worth now? If we assume about 3% (a pretty standard economic assumption) inflation the math looks like this $200 X ((1 + 0.03) ^ 35) = $562. I realize that this isn't a perfect extrapolation and that there are several arguments to be made here. However, I think that the main point still holds, which is if in 1978 the cost of a very basic bicycle was $200, you should expect to pay about 2.5 to 3 times that amount in todays dollars for a basic bicycle of similar quality.
So when someone tells me they want to spend $300 on a bicycle I just try to inform them of the type of quality they are getting, which is usually pretty poor. For someone who wants to go out with their kids and ride to the park and back, a $300 bike will work fine. For someone who wants to put in some serious miles, expect to be disappointed. Now, I'm not suggesting that you have to go off and blow $1,000+, although that certainly would expand your options. But in my opinion you don't really start getting into decent quality bicycles designed for serious mileage until you start looking in the $550+ range. Bikes go on sale just like any other consumer product, so that will relieve some of pressure on your budget.
Obviously, just my opinion.