We've all been in a situation where the roof is shot but another year would be nice. You can use asphalt patching compound to fill split shingles and seal most leaks, replacing shingles that are not repairable. Old shingles have a habit of disintegrating when you use a pry bar to loosen one for replacement, so be careful and use a very thin curved pry bar and take your time. Pay particular attention to the hips and valleys. Patch repairs will be visible, but should hold you a season.
As the weather dries, you might consider doing half the roof this year and half next. Usually the worst damage is on the South and West sides. You could change the roof on those sides and leave the North and East until next year. Choose a major national brand and style of shingle that has been around a while (and will be available next year). Go ahead and strip the old roof from the soffit to the peak on the side that will be replaced, make any sheathing repairs and put up the felt and re-roof. Breaking the project into two years is easier on the pockebook AND the back and knees. Good luck on the roof, I'm sure you can repair the worst of it and keep things within the budget. Keep in mind, repair and replacement of the roofing is usually a lot less expensive than water damage.