The answer depends on how much money you want to spend. If you have a crew of folks that you want to go riding with (and that's adviseable) put out some feelers and you should be able to come up with a bike that has a local history and will be reliable.
Modern 2 strokes are lighter than 4 strokes and easier to maintain. 4 strokes can be a little easier for newbies to get thier heads around in terms of power characteristics.
Kawasaki KDX 200/220s are great starter bikes, I wish I held onto the one I had. The power delivery on the 220 very mellow, and can be beefed up from stock quite easily with a few well documented mods. If you find a good used one, it is very likley it will have these changes made already.
One of the best woods bikes ever is the KTM 300 2 stroke. It makes power like a 4 stroke, is happy chugging around all day long at low speeds, but it will still drag you up the biggest hills you will find with ease. I must admit strong bias here, but if I had to buy another bike right now, it would be another 300. The KTM 250 has a more agressive power delivery than the 300 and is a little less friendly to newbs and casual riders. Still a very nice bike though. KTM also makes a 200, and it's very nice to, but it really likes to be flogged to go anywhere fast.
Again, in the field of 2 strokes, the Yamaha YZ250 can be turned into an excellent woods/enduro bike. Generally they are quite a bit less expensive than a KTM 2 stroke, but will need some mods to work in the off-road world. Tons of accessories etc available to make this happen too.
Once you have been riding a bit, take some time to get your suspension set up correctly. This does not have to mean sending it all off to a suspension guru and spending a ton of dough - there is a ton of info on the net about suspension set up, have a read, ask some questions and experiment a bit with the clickers. Good suspension set up is key to getting through the terrain safley and quickly.
Your terrain sounds a lot like what we ride here in the Interior of B.C. One of my favorite farkles is my Rekluse auto clutch. Makes steep stuff so much easier it's almost like cheating. Most of the guys that I ride with thought I was a wussie for getting one 3 years ago, now everyone has one!
2013 KTM 350EXC-F, 2005 BMW R200GS, 1984 Kawasaki GPz 750