ScoutmasterCG.com has a great Sleeping Bag Basics Info-graphic that I'm showing in this article. This can help provide a better understanding of the types and styles available and their intended uses.

Deciding on shape is based on the user and how they sleep.  Mummy Bags are more efficient at keeping the user warm because there is less air to warm with your body heat.  But Mummy Bags can be confining, especially if the user moves around alot at night.  Rectangular Bags work just fine, especially for non-extreme cold temperatures.  Do not consider a Long Bag until the intended user is 6ft or taller. There are 'Short' bags available for smaller users, but they tend to be Kids bags and are usually intended for indoor use only. Verify the bag is meant for outdoor use before buying.

For our climate and purposes, we recommend a 40 degree bag with a synthetic fill.  This summer or 3-season bag can be supplemented with an extra blanket in early Spring and late Fall months, but will work well for indoor and summer camping, without overheating the user.  If your Scout is often cold, consider a 30 degree bag. The synthetic fill will help keep the user warm even if damp, either from sweat or from high humidity or dampness within the tent. A synthetic or non-cotton shell and interior lining is also recommended for better performance. If your Scout already owns a summer or indoor bag, consider purchasing a 2nd bag intended for colder weather and then they can decide on which bag to pack based on the trip.

If you know that your Scout will be going on High Adventure trips, you might consider investing earlier in a more expensive "backpacking" sleeping bag that is more lightweight and will compress down to a smaller size.  It is totally understandable to not make the extra investment until the Scout is older and closer to their adult size. 

Some final notes:  

1. If your sleeping bag came with a storage sack, it is often low quality and just barely big enough to fit the bag only after the bag has been compressed to it's smallest possible size.  Often, younger Scouts struggle to get their sleeping bags fit back into the sack it came in on final camp mornings.  Consider purchasing a compression sack that easily fits the sleeping bag and then has compression straps to get the extra air out of the bag.  A waterproof compression sack is best to be prepared for rain when setting up or breaking camp as well as the first high adventure trip that our Scouts go on which is usually a canoe trip. To find the right size, Medium is usually best.  If you want to be sure, just bring your sleeping bag in it's normal sack into a retail store like REI and test out the different sizes to find a size that the bag will easily fit in without being overly large.  There are good choices online for under $20.
2. In addition, it's best if sleeping bags are NOT stored in their most compact form between camping trips.  Look for a "Sleeping Bag Storage Sack" on any online retailer and consider purchasing.  Again, a $20 investment can pay for itself by avoiding an early replacement.