Periphery
Not as rich, populous, or well developed as the great houses, the nations of the Periphery simply don't have the same wide variety of military equipment to choose from, and for the most part their heavier equipment has to come from the outside. As such, you should really choose from the normal universal list only sparingly (the universal infantry list is an exception to this. Most of those can be found everywhere, though artillery is more scarce in the periphery). The bulk of your forces should come from the faction specific lists detailed later, and this modest list of units widely available in the periphery.
Light Scout Lance (BM, size 1, 4 elements)
Movement: 6l 3j
TMM: +2
Armor: 7
Damage Values: 2/2/0
PV: 22
Bug Lance (BM, size 1, 4 elements)
Movement: 7l 2j
TMM: +3
Armor: 5
Damage Values: 1/1/0
PV: 19
LRM Carrier Platoon (V, size 3, 4 elements)
Movement: 3t
TMM: +1
Armor: 7
Damage Values: 3/4/4
IF Damage: 4
PV: 29
SRM Carrier Platoon (V, size 3, 4 elements)
Movement: 3t
TMM: +1
Armor: 7
Damage Values: 8/8/0
PV: 35
Medium Tank Platoon (V, size 2, 4 elements)
Movement: 5t
TMM: +2
Armor: 8
Damage Values: 1/1/1
PV: 20
Hover Tank Platoon (V, size 2, 4 elements)
Movement: 7h
TMM: +3
Armor: 8
Damage Values: 3/3/1
PV: 25
Attack Hovertank Platoon (V, size 1, 4 elements)
Movement: 8h
TMM: +3
Armor: 4
Damage Values: 3/3/0
PV: 17
Support Hovertank Platoon (V, size 1, 4 elements)
Movement: 8h
TMM: +3
Armor: 8
Damage Values: 1/2/1 (if 1)
PV: 24
Light Tank Platoon (V, size 1, 4 elements)
Movement: 4t
TMM: +1
Armor: 5
Damage Values: 1/1/1
PV: 15
Taurian Concordat
When I said for the most part the periphery's heavy equipment comes from elsewhere, the Taurian Concordat is the exception (heck, it might even be the elsewhere in some cases). Though described as a generally mediumweight mech force, the Concordat actually produces primarily heavy and light mechs, so... if you want to go for the mediumweight feel either you'll be using a lot of Griffins or you'll have to balance the two extremes.
The Taurian Concordat also operates six vehicles to a vehicle platoon. I've provided stats for these enlarged platoons in all the flavors you'd expect in Taurian space.
Finally, due to a case of unrequited love on the other side of space, you might find occasion to add a Steiner Medium Close Assault Lance or Steiner Heavy Armor Lance (Firepower) to your forces. I wouldn't use more than one of each in any given engagement. Just enough to confuse an eager young Comstar adept, but not enough to raise suspicion of some sort of secret construction program.
Heavy Battle Lance (BM, size 3, 4 elements)
Movement: 4l
TMM: +1
Armor: 16
Damage Values: 4/5/3
PV: 45
Heavy Fire Lance (BM, size 3, 4 elements)
Movement: 4l
TMM: +1
Armor: 18
Damage Values: 3/5/5 (if 3)
PV: 52
Medium Support Lance (BM, size 2, 4 elements)
Movement: 5l 3j
TMM: +2
Armor: 14
Damage Values: 1/3/3 (if 1)
PV: 40
Light Attack Lance (BM, size 1, 4 elements)
Movement: 6l
TMM: +2
Armor: 5
Damage Values: 3/3/0
PV: 20
LRM Carrier Platoon (V, size 3, 6 elements)
Movement: 3t
TMM: +1
Armor: 10
Damage Values: 4/6/6 (if 6)
PV: 44
SRM Carrier Platoon (V, size 3, 6 elements)
Movement: 3t
TMM: +1
Armor: 10
Damage Values: 12/12/0
PV: 52
Medium Tank Platoon (V, size 2, 6 elements)
Movement: 5t
TMM: +2
Armor: 12
Damage Values: 2/2/2
PV: 30
Hover Tank Platoon (V, size 2, 6 elements)
Movement: 7h
TMM: +3
Armor: 12
Damage Values: 4/4/2
PV: 39
Light Support Tank Platoon (V, size 1, 6 elements)
Movement: 5t
TMM: +2
Armor: 10
Damage Values: 2/4/4 (if 2)
PV: 36
Light Hovertank Platoon (V, size 1, 6 elements)
Movement: 11h
TMM: +4
Armor: 10
Damage Values: 2/2/0
PV: 32
Magistracy of Canopus
Canopus is a lover, not a fighter. Most of their mech production is light stuff, with only a trickle of mediums supporting it, plus whatever they can import (and their economy isn't great right now). So realistically you're mostly limited to what's on the general periphery list. But they are the only producers of heavy armor in the periphery, and they do import weapons from the Concordat...
Medium Battle Lance (BM, size 2, 4 elements)
Movement: 5l 2j
TMM: +2
Armor: 13
Damage Values: 3/3/2 (if 1)
PV: 37
Heavy Tank Platoon (V, size 3, 4 elements)
Movement: 4t
TMM: +1
Armor: 12
Damage Values: 4/4/3 (if 1)
PV: 37
Outworlds Alliance
It'll look better when I get to the aerospace forces. I swear!
Medium Striker Lance (BM, size 2, 4 elements)
Movement: 6l 2j
TMM: +2
Armor: 8
Damage Values: 2/2/1
PV: 25
Light Support Tank Platoon (V, size 1, 4 elements)
Movement: 5t
TMM: +2
Armor: 7
Damage Values: 1/3/3 (if 1)
PV: 24
Niops Association
A hidden gem, or a chicken bone to choke on. The Niops Militia is never something you run into outside of Niops. Which is probably for the best.
Heavy Lance (BM, size 3, 4 elements)
Movement: 4l 1j
TMM: +1
Armor: 17
Damage Values: 5/5/1
Special: prb
PV: 48
Light Lance (BM, size 1, 4 elements)
Movement: 8l 1j
TMM: +3
Armor: 9
Damage Values: 3/3/0
Special: prb, ecm
PV: 23
Heavy Tank Platoon (V, size 3, 4 elements)
Movement: 3w
TMM: +1
Armor: 10
Damage Values: 5/5/4
PV: 36