This is demo season for bike companies, so I would suggest trying a few out. Bikes have come a ways in the past 20 years. The choices vary quite a bit now compared to then, although at the $1,000 price point, not as much. Especially, if you're on the tall side, you may want to try something with 29" wheels. If you want a bike from the local bike shop, and all of the support that may come with it, then at least check out the big three brands (Giant, Specialized, and Trek), and whatever else your local shops carry.
If you don't necessarily need the higher level of support of your local shop, and can do some of the fine tuning by yourself (unless you're willing to pay someone to do that), check out Airborne's Goblin (it's a 29er). It's $200 over your budget, but the level of componentry (especially the Reba fork) can't be touched at MSRP prices.
If you're looking to be as economical as possible over the long haul, get the most bike you can from the get-go as upgrading things as you go gets very expensive in comparison. $1,000 bikes (which are still in the entry level IMHO) compromise the most on three very important components, the fork, the wheelset, and the brakes. Entry level bikes are called entry level a reason, and serve a good purpose in the evolution of a rider as they progress. They get you out and riding at a palatable price so you can develop your skills, while you also discover what niche of riding (and therefore bikes) you will eventually gravitate towards. The components function well enough for the average novice rider's skill level during the first couple years of riding. It also lets the entry level rider figure out if this sport is even for you at all, while not breaking the bank.
In the evolution of the average rider getting into the sport, this is the most economical way to get to where you will eventually end up if you stick with the sport, and that is on the bike that fits your developed skill level, and is more specifically suited to the type of riding you really like to do.
You (the OP), are a little different since you have actually spent a fair amount of time riding, and know more or less what type of riding you prefer, and are likely (if I can make some assumptions from what info has been provided) to regularly do, and would like a bike suited for this that you will keep for a while(?). If this is indeed the case, and you're going to spend much riding time up in the San Gabriel or San Bernardino mountains as you alluded to, I would suggest upping the budget so that you can get a bike that is not necessarily designed for the purpose of getting entry level riders into the sport. If you are looking at this as a bike to get you back into the sport, and then maybe be looking to get something better in 1-3 years, then the entry level bike is a good way to do it economically.
At any rate, I would suggest you do take advantage of of some of the demo rides happening this time of year through shops in the greater SoCal area.
Buying used is an option, but it can be a risky proposition if you're not patient enough to wait for the right bike that fits you well to come along (yet willing to pull the trigger when a truly good deal presents itself). There are plenty of good deals on clapped out, obsolete, and/or stolen merchandise that you'll do best to avoid, but there is a chance that you could score a good deal on a bike that is still near new and fits you and your riding style well.