In Latin, the infinitive is not used to introduce a reason, or "purpose clause" as a Latin grammar would put it. Here are some other options, which I will gear toward the (very broad) use case of English translations using the infinitive with a sense of purpose.
- Ut + Subjunctive
ut means "that, in order that" and introduces a subordinate purpose clause. The negative of a purpose clause is ne. An example:
Loquor ut meminerim.
I speak to remember.
- Ad + Accusative Gerund
Ad pugnandum aggreditur.
He comes forward to fight.
- Genitive Gerund + Causa
Debellandi causa venit.
He comes to conquer.
- Gerundive Participle with object
This one is a bit tricky: if you are speaking of an object on which something "ought to be done," you can modify that word with a gerundive. This applies well to your second example sentence:
Aliquid boni edendum volo.
I want something good to eat.
(This translation might be made better...comments welcome.)
- And my favorite... the supine!
The supine is an oft-disregarded form that, for most intents and purposes, is the same as the neuter singular passive participle. It is quite common in everyday speech (just read Plautus and see it appear every page) and expresses purpose with verbs of motion. This translates your first example well:
veni esum/laudatum/plausum.
I came to eat/praise/applaud.