Does anyone have any advice for a new player on what to do first with certain characters?

For instance: When ever I have Michael McGlenn in play the first thing I do is run him up to the Curiositie Shoppe to try and get a magical weapon, since I mainly use him to street sweep.

I think you have the right idea: playing initially to your Investigator's strengths. Of course, those strengths can often change over the course of a game as fortune and misfortune flies around them (and you end up with Sister Mary the Monster Hunter and Michael the Gate Hopper), but at the outset, you got a little time to figure yourself out.

If you have a "shopper"--that is, anyone with extra-card-draws (Bob, Monterey, Dexter, etc.) or anyone with decent cash (Jenny, Vincent, etc.)--use them at the Location that allows them to use their ability (their starting location, usually), or try to get them to the Curiositie Shoppe for Elder Signs or other goodies, or the General Store for weapons and Clue tomes, maybe a motorcycle.

If you have an Investigator that starts with a Clue advantage (Mandy, Pete, Joe, etc.) try to get them to a Location with enough Clues to get them to 5 (you should always start the game with one Location with 2 Clue Tokens after the pre-game Mythos card is resolved) and then get them offworld as soon as possible. A Sealed Location by Turn 4 is a BIG help. (Adjust tactics as necessary, like if you're up against Hastur.)

Amanda COULD get a Bank Loan and use the money at the Administration Building for ANOTHER Skill.

Compare your opening cards and cash, and if there is an obvious trade that would benefit the group--giving Michael a Unique Weapon that Monterey drew, getting Tomes to someone with better Lore--try to get those Investigators together in some mutually beneficial Location.

If you have a Tome or other Item that requires movement points to use, consider taking your first Movement Phase to rest "safely" in your stable starting location to use that item. Not only could you gain the Item's reward, but you might get a nifty first Encounter as well.

I don't know how many expansions you have, so I'm not gonna get more specific, but don't be afraid to experiment. There's a lot of Arkham to discover, and winning isn't everything: it's just one end to the journey.

Welcome to the Carnival, seang.