Raising Perigee
Vehicles leave the launch loop in an elliptical orbit with a perigee at 80 km loop altitude, a radius of 8458 km near the equator. The launch loop is very efficient and not constrained by the exponential Tsiolkovsky rocket mass multiplier, so launches to high apogee orbits cost less than double the cost to LEO apogees, and both are surprisingly inexpensive. Given an kinetic energy cost of $200/MWHr (perhaps $150/MWHr scaled by efficiency), the launch cost to a low MEO orbit (10 orbits per sidereal day) is $1.85/kg (!), and to a 10 sidereal day HEO orbit is $3.09/kg.
The far greater cost is apogee insertion; that requires either a capture system or an apogee insertion rocket. The delta V for the MEO orbit above is 439 m/s and for the HEO orbit is 25 m/s  17 times cheaper! High orbits are "closer" from a launch loop.
A one sidereal day construction orbit may be optimum for most missions; it "returns" to a perigee over the launch loop once per sidereal day; launches and returns can occur daily. Actually, not quite; the orbit "returns" about 4 minutes earlier per day, and "resyncronizes" to the solar day once per year. Solar days seem more natural because our lives are scheduled by the Sun, not the stars. Spacefarers will march to a slightly different drummer.
Here's a table of perigee delta V's for different destination orbits. I've chosen a perigee at 2000 km to avoid LEO debris and collisions; if perigee changes, apogee changes oppositely to keep the same period and semimajor axis.
orbit 
apogee 
launch 

period 
radius 
delta 
cost 

sid. days 
km 
V m/s 
$/kg 

0.10 
9790 
439 
1.85 

0.20 
20462 
307 
2.36 

0.25 
25088 
270 
2.47 

0.33 
32163 
227 
2.60 

0.50 
44746 
177 
2.73 

1.00 
75950 
114 
2.89 
construction orbit 
2.00 
125486 
73 
2.98 

3.00 
167032 
56 
3.02 

4.00 
204116 
46 
3.04 

5.00 
238200 
40 
3.06 

6.00 
270068 
35 
3.07 

8.00 
328935 
29 
3.08 

9.11 
359385 
27 
3.09 
moon/3 
10.00 
383039 
25 
3.09 

13.66 
473527 
21 
3.10 
moon/2 
27.32 
756599 
13 
3.12 
moon 