There's certainly a lot to be learned, this is a good place. First thing I'd do would be to check and tighten all of the hoops on both barrels, fill them with water and check for leaks. The bourbon barrel will be very unlikely to have any bacterial challenges, as the high alcohol content will prevent that for the most part. The wine barrel on the other hand, needs to be sanitized ASAP. A good long steam would be best, but if you don't have access to a steam generator, filling with a strong solution of potassium metabisulfite / citric acid mixture will do the trick, just keep it refreshed until you are ready to fill with wine. Alternatively, you could burn sulfur sticks in the barrels and keep them sealed up afterwards, I've not done this so can't offer much on that topic, and prefer to keep them filled with sulfite water to keep the wood soaked with sulfite anyway.
Both barrels need to be kept filled to keep them hydrated and the wood swollen and watertight until you're ready to fill. I'd assume that since they've both been used for a few years that you won't get much in the way of oak flavoring from them unless they are re-cooped, but that's a whole different topic.
Once filled, maintaining them is pretty simple, keep them topped up on a regular basis (monthly) and monitor the sulfite levels to keep them in the right range as well. You should be a able to get many more years of service out of the barrels if they're in good shape. The micro-oxygenation and concentration, in my opinion, makes a very positive and noticeable difference in wine as it ages in barrels. I'm certain you'll get lots more good advice and tips from other members here, there are a lot of us who have been aging in barrels for quite some time. Good luck!!!