Welcome to Portland! I live in Beaverton and most of it is really nice. Traffic driving into downtown Portland from Beaverton can be a little bit of a pain...but in my opinion the west side is the nicest. I work nights near downtown, so traffic for me isn't a problem. I guess it also depends were exactly you may be going.
ETA: I see now that you are planning on public transportation, so not so much of a problem.
There are many apartment complexes right off of the MAX line in Beaverton and of course Trimet buses can get you there as well.
I have a fantastic pediatrician in Beaverton... Metropolitan Pediatrics Westside (located off of Cornell Blvd.) has several that are great. They have a website you can google. I have 2 kids that I take there and actually switched to them after the 1st pediatrician we had with our first.
We go to Portland First Church of the Nazarene and love it. It's located right off of Hwy 26 (the Hwy leading into downtown from the Beaverton area). They are very family oriented and great in the children's dept. I don't know if you are looking for something different, but we really like it there. There are MANY christian churches though...we went to several after moving just "trying" them out for a good fit. I really think you just have to check everyone out and see what you like.
There is a Craft Warehouse (I think that is what someone meant by Craft World) off of 185th Ave. (It may be considered Hillsboro and not Beaverton, but it is only about 1-2 miles off Hwy 26). There are several Jo-Anns Superstores around, as well as Michael's. Peddler's Pack is a good stamping store, but really has limited scrapbooking supplies. Whimzees Scrapbook Studio is a great scrapbook store in Beaverton on Shaw St. off Tualatin Valley Hwy that has classes/scrap nights. I haven't been to those, but the store is well stocked and she keeps current products.
As someone else said, there are several Targets...no super-Targets in the Beaverton area. I think there is one in the Jantzen Beach area (near Vancouver, WA)...not exactly close (about 30-45 minutes from the Beaverton area).
Also, as someone said there are great Farmer's Markets in the area. They have one near the public library in Beaverton and it is great! There are also lots of U-pick farms for lots of produce.
Check out Tualatin Valley Parks and Recreation for activities for your kids. They have several pools and gyms with all sorts of activities. Depending on where you live, you may get "in-district" pricing which is very economical. How old are you kids? Just trying to think of activities and such for them.
HTH! Let me know if you want any other information. I would be glad to help you out!