Can you give us an idea of budget? Affordable can cover a pretty broad range. My gut feeling is try to find a good shop in your area and look for a full-suspension bike in the $1500 range. I hesitate to make specific recommendations, but the Specialized Stumpjumper FS Comp is a nice bike at a reasonable price. You should start to see this season's bikes go on sale in the next month or so and the savings can be a couple hundred dollars.
I have an old hard tail and my dad and sister have new full suspension bikes. Going up on an easy trail we are about equal. On anything remotely technical (meaning you would think twice before driving your Porsche up it -- yes I'm a wuss) either going up or down I'm working very hard to maintain balance and stay upright and they are just enjoying the view. On any single track trail, my 62-year-old dad drops me like a bad habbit going up hill. Going down he is usually waiting 10-15 min. (meaning his speed is roughly 2x - 4x mine). This was not the case on his older titanium hard tail.
There are lots of good options from many companies including Specialized, Giant, Fisher. Even bikes that seem identically spec'd may ride very differently, so see what feels good to you. 3"-4" of travel is probably sufficient unless you are looking for a DH bike or something to jump off of things. Check out the reviews at
www.mtbr.com, but take them with a grain of salt. A large percentage are posted by teens with too much free time, company PR reps and people with an axe to grind. Still a good source of info.
I would spend money on a bike with front and rear disc brakes. Discs give you the ability to easily modulate your speed, where V-brakes are more on and off -- I really wish I had these, the difference is huge. Budget for better tires -- many bikes come with semi-knobby tires which look cool, are generally light weight and are only for expert riders. Buy a good set of knobbys, but ask the shop what works well in your area as they tend to be somewhat condition specific. Also, plan to upgrade the saddle. Most bikes come with a saddle to match the relative price-point of the bike and that is not a place to save money and cut corners. I still have not found too many that I like.