For American English at least, your guess is correct. Colloquially it's completely normal to reduce it to /tə/ before a consonant or a vowel — including at the beginning of a sentence.
Pronouncing it /tu/ in something like "to aim," in normal conversation, actually sounds stilted.*
The one place I'm less likely to reduce it is at the end of a phrase, like both of the instances in this sentence: "I'd like to, but I don't know if I'll have time to." I would almost always pronounce those as /tu/.
Also - when you have two vowels in a row (like in "to aid") it may be pronounced with a glottal stop or more likely just a bit of glottal constriction (it's variable). I wouldn't call it a pause, but maybe that's what you meant.
*Edit - actually it's more complicated than this. If the following word begins with an unstressed vowel — particularly another /ə/ — then /tu/ does not sound stilted. In fact I find I’m pretty likely to pronounce it that way, though either pronunciation is still ok.
- to assume: /tu əˈsum/ seems slightly better. /tə əˈsum/ is almost as good.
- to imply: /tə ɪmˈplaɪ / is best. /tu ɪmˈplaɪ/ is almost as good.
If the word begins with an unstressed diphthong, /tə/ sounds more normal to me, but /tu/ is somewhat acceptable:
- to obey: /tə oʊˈbeɪ/
- to outlast: /tə aʊtˈlæst/
The worst-sounding case is /tu/ before a stressed vowel, as in the examples you gave, which are the kind I was originally thinking of:
- to aim: /tə ˈeɪm/. /tu/ sounds stilted.
- to implicate /tə ˈɪmplɪˌkeɪt/. /tu/ sounds stilted
Sorry if this is a bit confusing. This is an area of the language where there isn’t an absolute “yes” or “no” answer that applies across the board. It’s more of a continuum, where the two pronunciations sound better or worse depending on the sounds next to them, stress, syntax, and social context (talking to a friend vs. presenting a speech). And other speakers may have slightly different judgments from mine. Don’t worry about getting it perfect. The more English you hear, the more you will pick up these small distinctions.