Getting up to speed as a new boater is something that you can expect to take a year or more. The ideal situation is for you to know what is needed and then either be able to do it yourself, or be able to find a GOOD marine mechanic so that he knows what he's doing but you know know what he's doing too.

. Local word of mouth is priceless here. Once you know of a good candidate or two, talk to them about what the boat is doing and how they would price the work. Different ones will include different things in their "packages."
If it helps you to get a level set, if I were in your shoes with the same boat and took it to my mechanic and had him go over all the things I would want him to go over, and had him do an oil/gear lube change, filters, standard winterization, drive pull/alignment check, etc., I would expect to pay around $600, possibly a bit more depending on how many parts are actually needed.
If you're mechanical at all, you can change your own anodes easily and your own impeller for not too much work. Shop labor is going to run $80-100/hour for anything not included in "packaged" service, so anything you can do yourself adds up fast.
In any case I would expect the dying engine to need some troubleshooting, so I recommend you start out finding a mechanic and getting that issue resolved. Have him winterize it, change oils, filters, etc., then you can spend the winter relaxing & figuring out which things you want to tackle yourself next year. Another heads up, unless the previous owner(s) have already done it, you're likely going to have to do some work on the trailer too.
On the gas, what to do with it depends somewhat on how much is left. If its possible to burn it up and replace with fresh that's usually the best advice but if its really bad it could have to be pumped out.($$$). Whether to store over the winter with a full tank or empty is a age-old debate. I just go with whatever is left, make sure it has Sta-bil in it, and don't worry about it. But you're starting with an unknown so your situation is different.
Keep the questions coming.