Hi Hoboken. Do not fret. Seriously! You will get there. With the benefit of hindsight (just opened a foreclosed pool with the help of this board...and trust me, said pool was a black mess and the frogs are still "imprinted" with "home" and come back to sing every night even thought it's all clean now!) I would take a slightly different strategy with the pool guys in order to get some action out of them. Eg. don't ask for alternatives and don't give the impression you're open to the concept of washing.
Call one up and schedule an "opening" -- provided you've budgeted that much. Openings around here, which include taking out plugs, checking the equipment (which is then warrantied to work the rest of the summer), taking off the cover, power washing the cover and deck, doing 1 vacuum, etc. run about $350. It's worth doing the first time, because if you follow them around while they're opening, ask questions, and take notes, you will then know everything you need to know about your pool equipment. Budget about another $200 to get yourself a vacuum hose, vacuum head, extension pole, leaf rake, and possibly a leaf gulper if you think for any reason there are leaves under there, plus the tool to lock down the safety cover, plus backwash hose if you need it (eg. if it was a foreclosure and they walked away, it may have been uncovered for months; but if it was a short sale, it is more likely to have been covered at the correct time, etc.) Our service guy will bring that for you on his truck, which is the easy, fast way to get the basic gear you need.
Once they open it, and determine FOR FACT that the pumps are or are not working (and I'm betting they WILL work...no reason not to -- what are the odds of FOUR pumps burning out simultaneously on a short sale, NOT a foreclosure?!) then you'll know which direction to go next. If they're not working, you might then have to fall back and punt (eg. there are lots of pump tutorials online, read the brand name, model # and google.)
However, if the pumps start up, next tell them only that you'll do the chemicals once you assess whether or not you'd like to drain and clean it, or whether you'll instead just clean up the water (don't get into the whole BBB thing...just nod and say you'll call them soon) -- If there's not piles of leaves etc. on the bottom, just have them leave the filter running -- if there's a lot of debris and you have a main drain valve handle and a skimmer valve handle, close the main drain valve to prevent debris from the bottom from clogging the line. Make sure before they go that they show you how to clean/unclog the pump basket, and how to clean your filters. Do not encourage them to put shock in or to "balance" the chemicals. Just say you'll pay to have them back once you've decided.
Then, take the leaf net, and scrape it all the way along the bottom from one end to the other. If there's a feeling of resistance (assuming you can't SEE the bottom) you likely need to net up leaves, etc. If not, you can likely just get started on the shock process.
Be sure to get your TFT100 kit first to take an opening reading, and then post back here. Whatever happens, these folks will be able to guide you step by step. But first, the cover has to come off; the pool needs to be dewinterized; the equipment needs to be tested with lines open and water available, and you need to determine what kind of recovery you're up for.
With respect to drain and acid wash, if this is not a great time to do so, you don't HAVE to no matter what -- just live with a season of stains -- won't hurt anything and it will give you time to get familiar with your gear and brush up on pool school. Also, though I see the rocks, I can't tell whether your actual pool itself is vinyl liner, or fiberglass, gunnit, etc. Since your pool is free form, and that's an expensive custom safety cover, I am kind of guessing whoever first built it likely spared no expense, so your gear it likely tip top. Here's hoping, anyway
Best wishes and do keep us posted!