i had some [admittedly 20 year old] continentals in that condition, which were fine for a while, but became distinctly dicey when the weather got warmer, the glue started softening and the hills got steeper.
i'd recommend some new tyres or atleast regluing the base-tape.
i found vittoria rallyes [£10ish] to be lumpy and slidey in the corners. they also don't have replacable valve cores, which is important if your pump has a habit of eating to tops of the valves. it means you'll need to replace the whole tyre for the cost of a valve core [£1?]
tufos [£20] are much better in the corners and i haven't had any flats despite the amount of glass and crap on the roads here.
i haven't used tufo regular tape, but the extreme tape is unbelievably solid. it took me about half an hour to get a tyre off the rim. [feel free to interpret that as a good/bad thing]
fsnl
sparky