According to FM:Crusaders, Zeta Galaxy only started out as a solahma unit, and that was before the Political Century. It wasn't staffed just with old solahma warriors but also with freeborns and dezgra warriors. As the Clan grew after the Golden Century, Zeta Galaxy became a slightly more respectable unit with some better quality troops and gear. I wouldn't call it a solahma Galaxy now, on the grounds that it's not all solahma. However, this is quibbling over details; in the end, what you're asking for is what would have been in Zeta Galaxy, and I can help a bit there. Sorry for the incoming wall of text!
As of 3067, according to FM: Updates, the four Clusters of Zeta Galaxy were:
- 40th Mechanized Cavalry (30% omni), with 80% Clantech, 15% Star League tech, and 5% Introtech
- 229th Mechanized Strike (25% omni), with 85% Clantech, 5% Star League tech, and 10% Introtech
- 27th Battlemech Cluster (25% omni), with 95% Clantech, 5% Star League tech
- 31st Battlemech Cluster (20% omni), with 90% Clantech, 10% Star League tech
Omnis: On average 1/4 of Zeta's machines will be omnitech, and the omnis would all be Clantech (I think IS omnis ending up in Zeta is a one in a million longshot). Mechwise, I'd expect plenty of Hellbringers and Mad Dogs, plus some other older omnis that the Horses are noted as using: Summoner, Fire Moth, Kit Fox, Adder, Viper, Nova, Stormcrow, and Naga. As for Omnivehicles, the Epona is reserved for front-line Galaxies so it is probably rare to non-existant in Zeta. Similar goes for the Hephaestus. If there are any then they'd probably be in command units. Omnifighters would likely include the Vandal (an unpopular fighter among Trueborn), the Avar (an aging, borderline obsolete design), the Sulla (used as escort and ground attack), the Turk and Visigoth (both very common in most Clans), and the Kirghiz (an ancient, widely-spread machine).
Non-omnis: Corvis, Bowman, Thunder Stallion, Thresher and Stone Rhino plus a lot of generic IIC mechs. I think all types would be mostly older models but might include a small handful of newer ones. The standard Glass Spider is also very widespread so there are probably some in Zeta Galaxy. For tanks, the Horses like the Hachiman and Mars a lot, I could see them fielding plenty of Ares, Odins and Oros too. Maybe several Stars of Donars. There may be some Bellonas but probably not many. Because the Horses value the Athena so highly I'd have to say it's unlikely for Zeta to have them except maybe in a command Star. Svantovits, Maxims and Anhurs seem like likely infantry transports. As for Aerospace fighters, the Xerxes is very common among the Horses. The Hydaspes is the kind of old design that would turn up in Zeta. The Chaeronea, Tyre and Issus are widespread designs.
Star League tech: Basically just about anything that the Exodus might have brought with them. Whole Stars of Thunderhawks and Nightstars would be wishful thinking, I'd expect more humble machines like Hussars, Lancelots, Champions, Sentinels, Crabs, etc to be the most common. There might be a few Royal versions among them. For vehicles, the Horses are known to use lots of Burke tanks in their touman. I think vehicles like Lightnings, Chapparals and Magi are also good candidates. There are SL Aerospace fighters too, FM:U places many in the 2nd Line Horses' RAT: the Rogue, Swift, Zero, Hellcat II, Ironsides, Gotha, Ahab, Rapier and Hammerhead.
Introtech: This will almost certainly be of Star League origin. It might be old stalwart mechs like the AWS-8Q Awesome or STC-2C Striker, or old tanks like the Puma, Rhino or even the LRM Carrier. Again, anything that might have been brought on the Exodus fleet. Considering that a Smoke Jaguar garrison rolled out a Mackie for a Trial once not long before that Clan was destroyed, even a tiny number of ancient mechs like Battleaxes, Gladiators, Koscheis, etc are not out of the question.
Isorla: Throughout Zeta Galaxy you might also find a scattering of mechs from other Clans. It won't be anything great, it'll be the stuff that the more prestigious Galaxies didn't want and handed down to 2nd-Line Galaxies like Zeta. The Horses were engaged in very heavy fighting against the Fire Mandrills in the late 3060s. I'd expect the most prized isorla like Crimson Langurs and Warhawks to be snapped up by front-line Galaxies, but less coveted mechs like the Mandrill and Predator could be shunted down to units like Zeta Galaxy. The Horses also fought the Wolves hard, so you could be looking at a few Lobos and Glass Spider 2s. It seems likely that decades-old Ghost Bear salvage would turn up in Zeta, so the venerable Grizzly and maybe even the Kodiak. Finally, the Horses and Hellions engaged in 'Harvest-style' Trials in 3068 so that could bring a few mechs like the Snow Fox and Icestorm into Zeta's hands.
Protomechs: Being cheap and disposable, I'd bet on these showing up in Zeta to quickly replace losses. You'd be looking at the usual Orcs and Hydras plus a few Harpies and Minotaurs.
Battle Armour: Mostly standard Elementals with a few Gnomes. Unpopular Undines might get shunted down to Zeta too.
In general my advice would be to pick units that reflect Zeta Galaxy having low standing in the Clan and being near the bottom of the supply chain. If your force starts looking too badass or too modern, I'd swap out some good units for junk instead.