Review of "Res pulchrae intellegendus sunt"
First, the gerundive, like regular adjective, should match its subject in gender, case and number. In that case res is f. pl. nom., so that yields: "Res pulchrae intellegendae sunt". Second, I think you are right to feel the sound is somewhat not what you are aiming to. The tone of "Res pulchrae intellegendae sunt"is usually rather: "beautiful things should(must) be understood" than "they exist in order to ..."
There might be several ways to render "exists", depends on context. I suggest to use here a passive participle. A possible candidate would be creatae (*). To express purpose, or the "infinitive" of reason we may use several different constructions (also). Here, we are dealing with passive infinitive, so we can chose ut+subj format, we will end up with (the word-order is quite flexible):
Res pulchrae ut intellegantur creatae sunt.
Or, instead creatae, to simply use the the verb exsisto:
Res pulchrae ut intellegantur exsistunt.
(*) One may raise some valid philosophical argument against this selection, but "(in order)to be understood" is, for me at least, makes it good fit).