It seems that the closest historical armor to the suit you want is Brigandine. I don't even know if that's in a supplement, so I would just call it Studded Leather and that should be good enough. Maybe throw in some fancy materials like darkleaf cloth (+750 gp).
Armor is easy. Use the same formula as armor in the core rulebook. (Bonus) squared x 1,000 gp.
Adding any ability score, like STR, has its own formula too, but it's luckily the same one, (Bonus) squared x 1,000 gp, but when you add that to armor, you have a 50% markup, so multiply by 1,500gp instead.
Stealth is a skill. Price it exactly like Boots of Elvenkind which uses the same skill, but remember to mark that up 50% for putting it on armor too.
If you want it as clothing so anyone can wear it without armor proficiency, you can still do it, just start with some kind of outfit and apply the same enhancements and costs, but the final armor class would be lower.
Of course, this way it is always on, always using all 3 modes at once.
Your way would be to create it (either armor or a suit of clothes) with separate modes that could be use-activated but only one at a time. Pick your three spells, Barkskin, Invisibility, and Bull's Strength are good choices.
The formula is:
Use-activated: Spell level x caster level x 2,000 gp
And
Multiple different abilities: Multiply lower item cost by 1.5
Since all of these spells are 2nd level with a minimum caster level of 3, the price is 12,000 for the first one and 18,000 each for the other two. But that lets you activate all three and use them at the same time.
There is no specific rule for only being able to use one item ability at the same time, so we have to get into houserule territory here. But it seems like a fair thing to do would be to assume that at ALL times you'll have one ability activated, so the cost cannot be lower than that. In other words, if it was just a suit that gave a constant Barkskin 24/7, the price would be 12,000, and if you had one suit for each of the three "modes", you would pay 12,000 for each and just change your clothes when you want a new "mode". Changing clothes is irritating, so you could make this as 3 rings which you could easily change and carry, but it would still be 12,000 gp for each ring. Having it as a suit that does all 3 but only one at a time is not really much more convenient than carrying 3 magical rings. (As a side note, a person could make a suit for one mode and a ring for each hand for the other two modes and could still do all three modes at the same time). Therefore, with those considerations, I think just simply not charging the 50% markup is perfectly fair, since that is the price meant to let you have more than one ability active at the same time.