Having been in the Army for a little over 9 years, I can answer some of your questions. I hope to be in the Coast Guard soon, as I have applied for the Coast Guard's Direct Commission Program, and the board convened this past Monday.
You will get a military ID, yes, as will any children you have who are at least 10 years of age or older. I suggest you hang on to their ID cards unless you think they won't lose them, as there is a bit of drama involved if it is lost. Your ID card will entitle you to use on-base facilities such as the Post Exchange (kind of like Wal-mart on the larger posts, but without taxes), the commisary (grocery store-again, no taxes, although there is a small surcharge), shoppettes (where gas is generally cheaper that off-post), and, of course, your medical insurance. Now since I am not in the Coast Guard yet, I can not say for certain what medical insurance you will have, but chances are it is the same as the Army, which is Tri-Care. There will be numerous amounts of paperwork to fill out in regards to that, and most likely it will take action from you first on all occasions. You will also need to initiate paperwork for your dental coverage as well.
Now all of this sounds fine and dandy, provided you have a military ID card. Since you do not, you will need to get one. I know of no way for you to get one without going to a military installation that can issue you one. I recommend you do a search on google or similar search engine to find the nearest military installation. Any one will do (Army, Navy, Marines, Air Force, or Coast Guard, Reserve, National Guard, or Active Duty for all). Once you find one, try to get a live person on the phone and find out what documents you will need to show up with to get your ID card. Most likely it will be something to the effect of marriage license, birth certificate(s), enlistment contract for your spouse, social security cards, possibly more, but those are the basics.
As far as high and low points, well, as I see them, job security, you will always knw that your paycheck is coming in now and will be for months and years down the road. Medical and dental insurance, while paperwork intensive, is generally much cheaper than you could otherwise get. The oportunity to travel to new places that you would otherwise been unable to visit. Since your husband is not in the Army, Marines, Navy, or Air Force, chances are lower that he will have to go to Iraq or some such place, although the chance of that occurance is still there. And, also of note, and great importance to me, anyway, is the fact that while in the Coast Guard, your husband will find that his job actually matters and peoples' lives can be beneficially affected by his service on a daily basis.
Best of luck to you in the Coast Guard, hopefully I'll be joining the ranks of the nation's homeland defense force soon as well.