I have a 1250 as well and I think it is a wonderful tractor, although I often call it my Nightmare, because it confounds me on occasion.
This tractor is part of the Quietline series, and they have their own little set of quirks. As long as your engine is sitting on the table, it would be wise to replace the ISO mounts, because that will save your oil pan, and a lot of wear on the rest of the drive train. There is a modification for your engine cradle that should be done, then the rubber ISO mounts should be replaced. Here is a link that explains the procedure.
http://cubfaq.com/isomount.html New mounts are available at one of the sponsors above.
As for your gas tank, The external sediment bowl with shut-off won't work on that tractor. You need a new valve and screen that comes with it, and a new rubber grommet that fits in the tank to seal everything from leakage. The sponsors above will have them and here are the part numbers: Valve - IH-109042-C2 Grommet - 935-0149. I know you are concerned with cost, but this is a part that you don't want to scrimp on. Gasoline leaking on a hot engine could result in disaster.
As long as your engine is on the table, I would also recommend that you check your steering and front axle play. It is a lot easier to fix with the engine is out of the tractor.
http://cubfaq.com/axlepivot.html
I agree with another poster, that Deestones are an excellent tire for the money. You can check Carlisle tires as well. They are a good tire at a fair price too.
It would be good to get that gear oil out of your transmission/differential, and change hydraulic filter. NAPA or a Cub Cadet dealer will have the correct filter, and it is highly recommended that you use CaseIH HyTran fluid. It takes seven quarts. If you have a CaseIH dealer near you and a couple of clean and dry 1 gallon jugs, the HyTran fluid is available in bulk, a lot cheaper than quarts at a Cub Cadet dealer. It would also be good to check to be sure the cooling fan place on the drive shaft. This fan helps to cool the Hydro change pump. It is an inexpensive and easy fix when the engine is out.
There things that you mention, such as the exhaust that you will want to fix later. A muffler box, a new, correct muffler and installing the side panels, a little bit of 935 white and 483 yellow, and you will have one sharp tractor!