$300 will buy you a very rideable bike for light trail and general road use. At this end of the price scale, a little extra money buys quite a bit more durability and quality in the components, esp the forks.
Most of the major brands do good versions and Giant is highly regarded, they dont make bad bikes. Do check that the bike has threaded eyelets for a rear luggage rack.
Often you can get upgrades on a new bike, one of the best is to switch the stock tyres to something suitable for your needs. Knobbly tyres come as std but for mixed use, a semi-slick (inverted tread) tyre is more efficient. For pure road riding, a 1.5" slick tyre is recomended. Kevlar protection will see off about 90% of punctures.