Depending on how much time you have, rather than mere memorizing, I would recommend learning Latin the old-fashioned way, starting with the 5 declensions, the cases, verb conjugations, etc.
But in the meantime memorizing prayers by rote is fine especially if for liturgical purposes, or for formally structured prayers like the Rosary, for which you don’t need to be paying much attention to the meanings of specific words you are saying with each prayer, instead reflecting on each mystery as you pray Ave Marias out loud, knowing the content of the prayer even if not able to identify each & every particular word you utter.
Once you have Latin prayers memorized, they will roll off the tongue even faster & easier than English.
Why so much negativity here, see word “Latin” and go into a frenzy “must be a RadTrad who hates Vatican II, what’s wrong with English, God can speak English”, the OP clearly can speak English & is able to pray in English but specifically asked to learn to pray in Latin?
Do you have experience with other languages, esp. inflected languages with cases? Latin studies can leap faster when you have internalized the concepts of grammatical cases, number, gender for nouns & verb morphology reflecting concepts like person, number, tense, voice, mood.
My Catholic high school (well Jesuit HS…) offered Spanish, French, Italian and Latin. Students of Latin could easily pick up modern Romance languages (and other languages, esp. those also with inflected case systems from Ancient Greek to Russian) with a bit of self-study.
Spanish, French, Italian all dropped Latin’s comprehensive case system; people I went to school with who studied 1 of the other 3, with only English as native tongue, became adults without ever learning core grammatical concepts found in inflected languages like Latin, Koine Greek, Russian.
In terms of grammar, if you know any Greek or Russian that can actually be more helpful for Latin grammar than Latin’s own Romance descendants.
But modern Romance languages would still help with vocabulary & with verb conjugations, grammatical gender, etc.
English classes nowadays do a lousy job teaching grammar, even the messy grammar of English.
If English is the only language you know & only language you’ve ever studied (or not even studied besides learning it growing up), then it may be of benefit to study English grammar in depth first to be able to recognize a subject, direct object, indirect object, object of preposition, English verb tenses & moods, etc.
Working as a peer tutor in HS & college, I’ve seen many monolingual Anglophones starting Latin be unable to identify subjects & objects & verb tenses & moods in English, so it was no surprise they struggled to make sense of Nominative, Genitive, Dative, Accusative, Ablative; Infinitive; Present, Imperfect, Future, Perfect, Pluperfect, Future Perfect; Indicative, Subjunctive, etc… which aren’t that complicated beneath the surface, but can appear daunting at first if you don’t know how to express them in English.