Let's take a sentence from this beautifully typeset Roman Missal as an example (p. 46, end of §5):
In Missīs dē Passiōne Dominī, prō quācumque necessitāte, prō peccātīs, ad postulandam grātiam bene moriendī, ad tollendum schisma, contrā pāgānōs, tempore bellī, prō pāce, prō vītandā mortālitāte, prō iter agentibus, et prō īnfirmīs.
('In Masses on the Passion of the Lord, in any kind of necessity, for [the remission of] sins, for requesting grace and mercy in peaceful death, for resolving discord, against heathens, in time of war, for peace, for averting the plague, on behalf of travellers, and on behalf of the sick.')
prō expresses the idea of forward-standing, proportion and substitution, and is generally the right choice with simple nouns. With persons it expresses on whose behalf you're praying. With abstract nouns like 'peace, health, remission of sins' it expresses correspondence between the prayer and the thing you wish to bring about, which is fundamentally an exchange relation.
- Notice that the English translation 'for' generally adds the meaning 'for the use of; intended for', which the classical Latin preposition lacks, but that can sometimes be found in the more mixed, ”translated” kinds of Latin. And other times, it inappropriately makes the thing look desirable ('for sins', 'for necessity'), whereas in Latin it's about correspondence, proportionality, or even being necessitated.
ad expresses terminus and purpose, and is mostly used in verbal, gerundive constructions (ad aliquid faciendum). In some cases you will want to use this construction even when no need for a verb is felt in English. When designating application, like in medicine, the gerundive is not necessary.
- Notice how it's prō vītandā mortālitāte and not ad vītandam...: the former appropriately expresses ongoing graduality ('as much as possible'), while the latter would make it look like a project directed at a definite outcome ('receiving grace', 'resolving discord').
in is not found in that excerpt, but elsewhere. It cannot generally be used in the sense you intend, but expresses movement into or unto (in your example, 'money for, unto a cause' and 'a passion for, towards battle'). In the Missal, it's mainly used 1) in certain collocations like 'in honour of', e.g. sacrificium in honōrem
sānctī Patriarchae Jōāchīm; 2) temporally, in diē... 'on the day of', in Nātīvitāte(m) Dominī 'on the Nativity of our Lord'. The ablative answers “when does it take place”, the accusative “what occasion does it celebrate.”
Many more examples can be found by looking at prayer names in the Missal, which is easiest to do in this HTML capitulated version.