I love the Luchuirp, so here's some pointers. At least its what I do.
First up, get Construction. Not after Agriculture or Mining. Construction, first, turn 1, now. Then build Baxter and get him killing barbs. Fairly often I get him to Combat V before first city even finishes its first wood golem. Once you have Woodys you're all set. Very difficult to crack, especially on Defense. Then start Rexing, expand till you can't expand no more and get out Gifts of Nantosuelta. You want as many hammers as quickly as possible. Move them all to cap (or holy city or wherever) and settle them all. Guild of Hammers is the most important wonder you can get, and Engineering and Sorcery (via Elementalism) are your tech goals as soon as you have Construction. Fireball tossing Gargoyles have your defense all sewn up, and hordes of Fireball Iron Golems backed up by Mages/Adepts with at least Enchant1 will win you the game. Use 1 or two of those popped GPs to construct the Tower of Elements for extra firebally goodness.
As for the Golems themselves...
Best Golems are Mud Golems. Throw in Nox Noctis, Blasting Workshop and/or Ardularia Chamber and they hold the title for best unit in the entire game.
Wood Golems are solid, but you want to replace them as soon as you can. But you'll be teching hard towards Engineering so thats not all that far away.
Gargoyles are the best defenders, and potent on the offense (better than Woodys anyways). These will be your main defenders for most of the game, possibly replaced by Arquebus.
Iron Golems are the workhorse. Tough, dependable, reliable, they will be your main unit. With the GoH you can build them in any city straight away. Use them, use lots of them.
Clockwork Golems are a mixed bag. On paper they are awesome, in reality however. They are expensive, collateral damage is pretty useless thanks to all your fireballs and can be killed on couterattack fairly easily (Easier than Iron Golems anyways). However that 15 attack strength makes them excellent spearheads to your golem army, and the tech is just one along from Engineering and gives a free GE as well as better windmills. For that reason, I usually have them running around before I have any Iron Golems.
Nullstone Golems are great. One of the best counters to Acheron or anybody with alot of magic, as well as providing a great spearhead along with the Clockworks.
Bone Golems are pretty meh. Immortals are cool, but Golems get no promos so a bit of a waste there, and getting the tech to build them is probably the most expensive tech in the game (especially if you're running CoE which means Theocracy is 15000 beakers of nothing). Cannabalize is useful if defending from a Counterattack, but you'll be fine without them.
Religions? Any work. RoK is one of the better synergies (Bambur teamed with Barnaxus is incredibly strong before you get any fireballs) but CoE is the best. Dwarven Shadows + Dwarven Druids + Gibbon (Twincast Earth Elementals with a spellstaff? Yes please) will complete your assault force. Hoard that Earth Mana and your repair mages will have free Earth2 for extra longevity and your Earth Elementals and Dwarven Druids will be even stronger for each source. Suffice to say, the Luchiurp need not spend anything on that expensive Religious tech line and still have one of the better fighting forces.
The biggest downside is Mobility, but Garrym Gir can use my Super Cavalry tactic, at least on the hornguards so that can give you a little extra punch at rage, but generally you can just fireball anyone/anything into submission from 2 tiles away so you're basically fine.
And be very nice to any Sheiam nearby, at least until you have Gargoyles. After that with Palace life mana and beeline to Sorcery your mages can wipe the floor with them.
Any questions just ask.