A few years ago Mrs. Jayer declared us too old to haul suitcases up and down subway stairs. By now I even agree with her, and we do a taxi. So this reply is conceptual and historical. You should check the current transit map and bus schedules.
What's the fastest way to get to this hotel via transit from LaGuardia?
Pre-remodeling of LaGuardia, the Q70 (recheck number) was express or semi-express bus service to the Queensboro Plaza transit hub (with several choices into Manhattan). The M60 was express or semi-express bus service to 125 St. and Lexington in Harlem (Lexington Avenue Line), after passing under what used to be the E Train (which I believe has been renumbered, in Queens just a bit before the river--I think, but don't warrant, at the Astoria Ave. stop).
Also dated content, but the express buses required you to pre-buy a higher fare and show a receipt, rather than just swiping a Metrocard. Which made no sense. (Especially since half the New Yorkers just boarded through the back door and didn't pay anyway).