What advice do you have for a newlywed dual-military couple? What should we expect moving forward?

Live for the time you do have together, learn to stay in contact even when separated. No matter the size of the gesture or the miles apart.....the smallest bit of contact makes a difference.
25 years, my wife was gone 18 months Desert Shield Desert Storm, I was gone to Iraq 3 times Afghanistan 1...add in hundreds of training deployments, thousands of early mornings and late nights.. 3 years as a company 1SG, 3 years as Drill Sergeant, 7 years as an SGM ending as the Div G3 SGM...
We made it work because of the above.
Anything from a phone call when gone, to having a friend who is still at home, drop off a cup of starbucks coffee to her while at work. I've appealed to internet acquaintances on forums I frequent to take flowers to her... The what doesn't matter, just that you did.

If you find you will be separated a lot, separate banking accounts.. helps not double spend money... Or three accounts..a main one boths paychecks go to, and then a allotment of "spending money" into the sub accounts..Bills are paid from the main.... coffee and gas from the sub.. New gloves or Sunglasses from the main but only after discussion.

Live within your means. Keep each other informed in regards to upcoming events. Forecast time together based off both training calendars.

Sorry if I drone on here. Being dual military is a very difficult task at times. You need to have a good relationship with each other, talk honestly with each other and your career guidance team/branch managers. I know many people who have done well with it but it takes management, patience and perseverance. I have spoken with many West Point 2LTs who get married after graduation about some of the pitfalls and temptations. It will be a tough road - but you can make it work. It is important that you schedule time on your calendars for each other. War-Story: During our first rotation to West Point, I was in the field or Deployed when my Wife (also in the Army) had free time. When I had free time she was busy with her unit. Rewarding assignment but taxing on the relationship. There will come a point where you have to decide whose career comes first. I know quite a few dual military couples that have split (even with children) because of too many competing demands and/or career goals that they did not discuss. Marriage is absolutely worth it - but it will take work. Good luck and get enrolled in the Army Married Couples program as soon as you are married and keep your branch team apprised of your situation.