Hello and welcome, nice you have an explorer, I know you will have great advise from all here mate.
Regarding the noise, with the Explorer, I would really suspect the timing belt tensioners rather than tappets, you see a mechanic who never knew explorers would probably say it was tappets..............but and here is the crunch! Tappets can run for thousands of miles before damage to the engine, on the other hand the tensioners and your timing belt will not if they are that bad.
The best thing to do, if you are handy with a spanner and a basic tool kit is to do the oom12 job, you will find many write ups here and a few with detailed pics also, that would at least stop te fear of a wrecked engine.
If it still makes noise after this I would get a decent engine flush and run that then do an oil change with new filter using a good quality oil, after that feel free to say its tappets ..............( by the way tappets would probably not hit the rocker covers, they cant open that far, tappets make a noise when the gap between them and the cam is too big, this would cause wear on the tappet seating surface and in time in the camshafts), and have them sorted.
Regarding price, the kit I mentioned contains everything you will need to do the job on the left hand timing chain, a brand new redesigned tensioner to take up the slack in the timing chain and replacement upper and lower intake manifold seals and an oil restrictor to keep the oil at the top near the chain, Howard can get you the parts, search him out on this site, he may even do it if he has time, PM him and see mate.
I do not know how much tappets will cost, but you have to be careful, as I do not trust garages at all, they may say its your cams that are toast and then you are looking at a major expense!
Do things in the order I suggested please or you may end up with a car you cant drive!
If you need further advise, I would be more than happy to help mate, I have only just done my own oom12 kit as my engine was rattling a bit too.................now its perfect!