Sadly, the most influential book on English Grammar does not accept the unqualified statement Prepositions are followed by a noun phrase or pronoun. It accepts the idea of the subset of 'intransitive prepositions' which are obviously not followed by a noun phrase or pronoun, citing the similarity of structures such as:
He had never been abroad before the war.
He had never been abroad before.
However, many grammarians do maintain that this analysis is imperfect.
If we accept that prepositions need a following noun group, before is readily classed as a preposition in the first sentence here and as an adverb in the second (compare he went abroad later).
However, this isn't a complete explanation either. In
The ship hove to.
The 'to' is obviously not a preposition - but it cannot be dropped from the sentence without leaving an ungrammatical residue. This is different from the above example using an adverb:
He had never been abroad before.
=> He had never been abroad. (OK)
In such cases, an analysis I subscribe to is that the 'heave to' construction cannot be separated into different parts - it's a multi-word lexeme (cf 'ship of the desert' for camel). If the 'to' in such a structure needs an individual name, the one it usually ends up with is 'particle', or, to show its affiliations, 'adverbial particle'.
I'd argue that 'bring to' and 'fall to' in Shoe's examples are multi-word lexemes.
A drop of whiskey brought him to. *A drop of whiskey brought him.
Fall to! DM:Fall!
Examples of to as a true adverb don't seem very common - but he may have found one in 'She pushed the door to.' But perhaps this is better analysed yet another way, as a directional / locative particle: 'I think she pushed the bolt to/home. Is it home?'
Apparently, a nautical expression uses 'to' as meaning 'into the wind', so this is (arguably! - how cohesive are turn and to here?) an adverbial usage:
We turned to and flew as much canvas as we could manage... (Google)
Best Answer
The grammar aspect has been sufficiently addressed by John Lawler in the comments.
These ngrams show that there is a slight popularity advantage for the variant without to, both in individual occurrence as in number of ngrams found at all. Dwelling on the popularity for a moment one might also show these ngrams showing the overwhelmingly more popular usage of provided us with. Thus, one could say the most idiomatic wording of your sentence would be this: