Hi! Welcome to Portland (can I say that if I don't live there anymore?).
Congratulations on the job at MMC. You've successfully avoided one of the most difficult parts of adjusting to life in Maine as the job can be tough to come by.
I think you have the right idea with renting first. I would check
craigslist.org for private rentals (they also have some companies too) as you can find MANY good deal via that community (that's how I took care of all but one of my Portland rentals). My favorite management company to go through is
H.H. Sawyer and Daughters. They tend to have the best prices and really avoid the B.S. when it comes to hidden fees and additional costs.
Port Property Management is the one I avoid. They have a lot of properties and some of them are very nice, but the advertised rents are never what you end up paying. They add in some insane fees (i.e. $10 water surcharge/month, $25-100/mo pet fee, $25 lawncare fee, $10 Sewage fee, etc) in addition to the fact that no utilities or trash removal are included. Again, I don't know what your budget is and they do have some nice properties, but they do nickle and dime you to death.
Now, as far as locations to live go, there is no such thing as a "Bad" or "Dangerous" Portland neighborhood. Bayside is a bit run-down and industrial, but that's about as bad as it gets (trust me, REALLY not bad). Furthermore, Portland is small enough that it gets "burbish" (almost rural in spots) within the city itself. In fact, there are really only about 3 or 4 neighborhoods (aside from downtown which has a small geographic footprint) that would really constitute "urban" (i.e. nearly wall-to-wall buildings) and those include, Munjoy Hill, Parkside, West End (only parts of it) and a LITTLE of Bayside. Other than those 4 areas (and downtown of course) the city is suburban in set up. Oakdale, Rosemont, Deering and Back Cove are really old style suburban neighborhoods. They're quite nice, actually. They are loaded with some nice older homes (lots of Victorians) complete with little yards and quiet, tree-lined streets. As you get out towards the Westbrook and Falmouth town lines, the neighborhoods are more of those 1950's and 60's style smaller single family homes. Close to the city lines there are many neighborhoods that abut large tracks of open, undeveloped land. In short, you can live in various types and densities of neighborhoods within the city limits.
For you, I'd say the
West End would be ideal. It's a charming neighborhood with some incredibly beautiful old homes (many of them now house rental properties) and great, quiet streets. It abuts Downtown Portland on one side (furthest East) and Maine Medical Center is sort of smack in the middle of it. From most areas in this neighborhood, you could walk to work. Parts of this neighborhood (particularly closest to downtown) have densely packed homes, but much of it has a more suburban feel.
Parkside would also put you within walking distance of both downtown and the Medical Center. It has an abundance of rental units.
Munjoy Hill is very pretty and only a quick drive (or bus ride) to the Medical Center. This neighborhood is on a hill and affords stunning views of Casco Bay. If you can get a place along the Eastern Promenade (many units are affordable here), you wouldn't regret living a bit further away from the hospital.
For a bit more quiet, check out some of the rentals in
Oakdale (near USM),
Deering and
Back Cove. These neighborhoods are old style suburbs that are still VERY close to downtown Portland and Maine Medical Center.
If you're looking for a newer style suburb, there are a large number of newer apartment complexes in Scarborough, Yarmouth, and Falmouth. These towns are very close to Portland and you would have easy access to MMC (which is JUST off of exit 5 on I-295). South Portland may also have some good rental options too. I'd look into the area of South Portland near SMCC and Willard Beach as it's very pretty.
Good Luck!