If you take a job as GM of the giants you're not doing it to win next year dude. everyone understands there's a mess to clean up.
With that said, Daniel Jones isn't THAT bad. He's a serviceable fringe starter who would play a lot better if he had time in the pocket. If I'm taking over the Giants my first thing to fix is the OL. They have a strong-when-healthy running back and a QB who's getting destroyed on the field. OL is priority #1 to get that offense working a bit better, and I don't think you need to bring in studs to see improvement on that line, just bring in some young players with some fire and a OL coach who knows what he's doing. so that should be an area where you can make real improvements on a tight budget.
Defensively I'd prioritize a shutdown Corner in the draft and work on the linebacker corps. Again, this is an area where you can make some additions by subtraction fairly easily, especially with a good DC and secondary coaching. The short term goal is to limit the opponent's ability to make chunk plays, so Corner and Safety are the two most important positions on defense.
If the goal isn't necessarily to win next year but instead to make multiple fundamental improvements to the Giants roster, that should be doable, especially if you can bring in some good scouts from the old org.