IMTU, Space Rescue is part of Commo Branch of the IISS. This is becuase there is a type S stationed at almost every inhabited world in the imperium.
Many mod pop worlds will be slated a "Rescue Cutter": 300Td, with three docing ports. Above and below are multi-dock folding cradles (2T each) configured for Types A, A2, S, S2. In the aft center is a 1T for an X-boat. Clean performance is 6G J1.
Orbit Control, COACC, and Customs are usually local, but may be imperial loaners (type T's) in no/low-pop worlds. COACC may be sysNav or a separate service. On smaller pop worlds, the navy's patrol fleet will be present.
Interdict, syspat: ModPop and HiPop worlds will have system squadrons doing these, and may also be doing customs.
On-planet resuce is Army/COACC.
I figure SysNav at 1Cr of Maintenance per year per person. That works out to a hull budget for on-station of 1KCr per year. (Local Naval Tax is usually double this: rest is salaries and construction.)
The Starport may have an additional customs and rescue fleet of similar size. It depends upon the noble in charge. He also gets Cr3, but tends to spend Cr1 or less on maint, similar on mobile asset admin, and the rest on Dirtside facilities.
The local count may also have a similar assessment. He'll spend Cr1 on troops, Cr1 on Naval Admin & construction, and Cr1 on Naval Maint. His forces float, usually about half the tonnage (and 1/3 the hulls) around his seat.
The Subsector Duke does likewise, but his ships tend to be mroe military.
The Sector Duke also has a Navy... he runs the local sector navy, aka Reserve Fleet.
The Imperial fleet budget is Cr1/head for maint, and Cr1/head for admin, and Cr1 for Hull Replacements. Double this in wartime.
The scouts get Cr3 per head. Cr1 of this is fleet maint. The rest is hull replacement, salaries and facilities.
The Marines get Cr1 per person, for salaries and equipment. Considering it costs MCr0.5 to train and equip a Cbt Armor Marine, plus he draws a salary of KCr3-10 per year it takes KCr130 per marine. Or roughly, 2 per 300K people. Battle Dress troops are about quadruple that cost, counting grav belts, BD, optics and commo, and heavy weapons. So 1 BD takes the levy from 1million people. (Amortize the equip ver 4 years. WIll usually have excess equip, but the excess is lost to admin and maint.)
The "Imperial" Army is a subset of troops maintained by the nobles levels, usually Cr1/head of their Cr3 assessment.
Typical troops take about KCr20 to equip, and make 3K to 10K per year. costs range from from 8-15K per year for line troops. Armor is WAY more; amortized over 10 instead of 4, and at 2-5 troops per vehicle...
Systems with ModLaw+ may have separate Customs Police, drawing Cr2/head, again 1 maint and 1 admin.
This doesn't count local planetary armed (Army and wet-navy) forces, just the imperializable ones.
Oversight Fleet: Every inhabited world gets assigned an IN Type T, and every subsector an additional 3-4. Mod Pops get 1-6, High Pops are assigned 2-12. These can be used to assist local customs, or to do anti-piracy; their prime mission is Anti-Rebellion alerting. If a local world denies imperial authority, or violates the rules of war, the oversight fleet jumps out to bring in the main navy.