There are many, many threads in each SA forum about post-grad education. All have excellent opportunities, and there are many options.
Use the Search function and browse, since this topic comes up regularly.
Officers, to promote to the higher paygrades of O-5 and O-6, are expected to have a Master’s degree.
There are full-time student
“duty under instruction” orders to places like the Naval Postgraduate School, Army War College, Navy War College, AFIT, National Defense University and others. There are options for civilian schools. For Navy officers, that opportunity comes during the first or second shore tour in between operational tours.
There is also the option to do distance learning with the Naval War College and others, or attend after-hours local NWC classes in Navy homeports such as San Diego.
There is Tuition Assistance, which pays for after-hours programs and distance learning while assigned to regular duty.
In general, degrees obtained on the military dime must relate to military skills sets. There is usually either a concurrent or consecutive additional service obligation time involved.
If you pay for it yourself, in an after-hours program, there is no service obligation.
USNA also has a small number of mids who are able to get their master’s by finishing their undergrad early, and while still a mid, attending classes at GWU, Johns Hopkins, etc., graduating with their class and finishing their advanced degree by Dec of their class year. There are also programs for 1-2 year degrees at Oxford, Cambridge, Naval Postgrad School, others, and mids have successfully competed for Rhodes, Fulbright and other programs. Mids get plenty of briefs about this. Warning: these programs all depend on the needs of the Navy and Marine Corps, so availability out of USNA can change. These officers also join the Fleet or Corps 1-2 years behind their peers, in terms of warfare qualification.
The other SAs will have similar programs at various stages.
If you serve the required number of years to receive the full post-9/11 GI Bill benefit, you can use that after separating anywhere you can get in, including top-ranked universities which offer additional scholarships to veterans.
At this point, I recommemd choosing your commissioning source based on Service and military specialties that interest you. You will learn all about all of this as you go.
Each Service has plenty of opportunity. You’re expected to be a warrior first, able to perform in an operational setting. Additional education comes along later.