If you want to go the budget route, swap on the heads, intake, and throttle body from an early 90's explorer or Mountaineer. The stock cam can easily take you into the 12's and retain normal driveability with a set of 1.7 RR. Those heads are the same as gt40's and all you should do is swap out the springs, and check the valves and guides for wear. The throttle body is 65MM and is easily adapted to the Mustang. Add a 94-95 Mustang gt 70MM MAF and you will end up around 270 hp for about 400-500.
If you want to step up from there,IMO about the worst cam choice you can make today is to put a Ford "letter" cam in your 5.0. That technology is over 20 years old and I rarely see a cam that has all of the same lobes. Sure, they may make a nice lopey idle, but for the same price or a little more, you can get such a better cam from a number of companies- Anderson, TFS, Steeda, and of course Ed Curtis.
For heads, I would either save up and get a quality set from either AFR or TW. You can pick up a nice used set for under $1000 often with RR . If you want a top end kit that produces a proven 350 HP for about $2500, get the TW top end kit from Summit. It comes with heads, cam, RR, gaskets, pushrods, etc. I think the only think you would need is the MAF and you can still use the 94-95 Gt one.
Regarding hydraulic vs. flat tappet cams, the difference is essentially that the lifters on a hydraulic cam self adjust with a plunger and spring. Once you set the initial preload, you don't have to readjust them. With a flat tappet or solid lifter cam, you will have to keep readjusting the lash or load of the rockers periodically. Think of the difference between the self adjusting belt tensioner vs. the manual belt tensioner on most supercharger setups. As the belt gets older and stretches, you have to keep readjusting the tensioner to maintain the proper tension. Unless you have a dedicated high rpm drag car, there really is no advantage to a solid lifter cam on the street, and do you really want to have to remove the intake, valve covers, and such for routine valve adjustment? You'd also have to buy a new set of solid lifters, pushrods, rockers, etc for that setup.
Whatever you decide, don't start throwing mismatched parts on as you will be disappointed with the results and could end up damaging your engine by not checking clearances.