One of my players, playing as a transmutation wizard, has interest in working towards building an iron golem or animated suit of armor, either of which being sentient and containing an actual soul within. 

I would like to offer the possibility to the player so they have a side goal to work towards during the campaign, but of course given the potential payoff I want to make sure actually building the companion (or party NPC) would be a challenging feat.

I was wondering if anyone had ever done something similar in a previous campaign and how they handled it. Of course, with the idea of binding an actual soul to the creature, it would be more difficult than simply building a golem or animated suit of armor, I expect.

The DMG provides some good starting points for this kind of thing in the magic items section under the golem manuals. Notice that the price tag is very high, from my way of thinking a player would be better served "bang for buck" wise spending that kind of moolah on something like an army of tens of thousands of normal soldiers. But golems are cool, and immortal, and you don't have to pay them so I guess it ends up being a better investment in the long haul, whatever. Lets get back on track.

Start with the hefty price tag, this cost probably represents stuff like laboratories, magic gems, widgets, lighting rods, assistants, special clays, metals or what have you used in creating the golem. Just getting this stuff together could comprise several adventures, finding a secluded area where the magic cops aren't gonna come knocking to bust up your illegal golem making den, or getting the licenses from the local government to build golems if a character is more lawful minded.

The soul binding idea adds a little flavor. Depending on what soul is bound to the golem it's stats might change, imagine binding a manticore soul, or the soul of a great long dead warrior, or tracking down a demi lich and sticking his soul in there, something like that. Use the spell Soul Cage, I think it's Xanathar's.

So yeah I would say there's seven steps:

1 Set up laboratory/work area thing

2 Build the Golem shell

3 Learn the spell Soul Cage

4 Hunt down the creature whomsts soul you wish to use

5 Kill that creature

6 Steal its soul with the Soul Cage spell

7 Implant said soul into golem

Golems as they are in the MM are powered by bound elemental spirits and have no initiative of their own, they are automatons that take orders literally. If the player wants it to be sentient (I assume the word sentient is being used in a more casual sense to mean that the golem would have the ability to understand the spirit of an order, that it would be able to act on its own initiative within the constraints of its creators will)  then I would make some kind of trade off for the "sentience" aspect of the golem, like make it targetable by dispel magic, something like that.

I wouldn't worry too much about the increase in power a golem will bring to the party, if they're at the level where they're building golems, and dumping 60k+ gold on golem factories then combat encounters weren't gonna be a challenge anymore anyway. D&D at this level starts looking less like lord of the rings and more like a pulpy, over the top, 80s techno cyber spy thriller, scrying, counter scrying, teleporting your golem swat team into the enemy base, that kind of thing.

Anyway that's my ramble, probably went longer here than I should have but it's not like I'm getting charged per word so there ya go.

Terrific help. I will keep your tips in mind when formulating a plan