(I had to ramble at the beginning. For the quick answer, please go straight to the last part.)
「させていただく」 is (or was) indeed a "controversial" honorific phrase among us native speakers. It is, however, so incredibly wide-spread now that we do not even discuss it often anymore.
If you search 「させていただく」 on Yahoo Japan, many of the first few hundred hits are indeed regarding this controversy itself.
The point of the controversy as viewed from the perspective of the opposing faction is that the phrase is simply too artificially and overly humble while yet sounding kind of pushy with a "weird" combination of causative and humble.
「させていただく」 simply means, or is supposed to mean, the same as 「します」 or 「いたします」. Until a couple of decades ago, therefore, using 「いたします」 was regarded as 100% polite enough for business use, so it was what most people/businesses used for humble and respectful speech. Some people, however, still strongly believe that 「いたします」 is humble, polite and respectful enough, hence the above-mentioned controversy.
A couple of decades ago, some people -- perhaps some large and influential corporations -- started using 「させていただきます」 in speaking and writing to their customers and it caught on very quickly, resulting in "everyone" using it in no time. The expression was new and it sounded very nice and polite to many.
「～～させていただきたいと思います」 literally means "I think we would like to kindly receive the favor of you graciously letting us ~~." No wonder why there is a controversy, eh?
Thus, the sentence in question means:
"And now, ladies and gentlemen, I think we would like to kindly receive the favor of you graciously letting us start today's banquet."
I trust that you could easily rephrase that the way it would sound more natural to English-speakers.