Buying the HP items is legitimate and it's a pretty common choice.  Just not my fave.  If you play smart, you won't need the extra HP.

There is a middle path, one I take sometimes.  I'll buy the 250GP health potion.  This will save me in a pinch, it's cheaper than the armor.  Also, it allows me to convince enemy demigods to overextend.  I'm at 25% health, Unclean Beast thinks he has a kill so he follows me into range of friendly towers.  I pop my potion then pop the beast.  250GP spent, 1400GP earned from the kill.

This is sick, I once had a level 15 Reg with some 580 damage per shot, 0.65 refire rate... killed towers like they weren't there, murdered demigods like they're made from paper...

Mines are really effective against DGs when your opponents are distracted or you are playing with an ally who provides a large shadow like Rook or lots of confusing ground coverage like a minion General..

Stats/Slow Reg is ridiculous when he reaches critical mass, but I wouldn't use him in every situation.  Sometimes a snipe/mines or MoB build can be more desirable..

At max level they knock off half a Demigod's HP just by tossing them at their feet, and it slows them to a massive crawl. Mines are great, but you need to invest the skill points.

Mines are harder to use but can still be very effective.  Just throwing them at enemies won't do much unless they are already weakened.  Setting up mine traps in good places works very well though.  Setting up traps can also be used to protect yourself from melee demigods like UB that would usually tear up Regulus easily once they got close. You lose effectiveness against ranged demigods, but you gain against melee demigods. 

I'm not sure how important Divine Vengeance is to Reg.  If your team is having trouble killing creeps, it's pretty essential.  When it comes to killing other demigods though, it might be easier to put the skill points into passive skills and money into speed/damage.

DV is awesome, but you must control yourself, unless you really enjoy having an empty mana bar. However, once you get the 10% mana per shot weapon, you can flick it on and forget to ever turn it off. If you have the money, that is.

even the Level one mana helm will last you well into level 5.. with a refire rate of say 1.2 (average start) you dont use that much mana.

I find with Regulus, getting Swift Anklet, Boots of speed, and Wand of Speed are the 3 most important items to you. regulus is all about dictating the range, and rules of engagement, and with 9.5 speed, who can argue? - it also makes you THE guy to farm creeps, and spend some of your gold on things that will help the team (totems of revelation, Capture locks, dropping potions)

It's pretty easy to have a build with lvl 3 mines (1350 damage + massive slowdown), maxxed snipe, and maxxed divine vengence - thats how i tend to focus, DV first, then some snipe/mines together

I've recently been having success going:

DV followed by 1-2 points in stats, then max out DV and Maim and then Sniper's Scope. I use a combination of the Swift Anklet and Boots of Speed (Though I'm considering just saving for the Wyrmskin Gloves) to get out there, cap a flag or two, then kill some creeps for an easy level 3. I try to avoid fighting enemy Demigods until I'm about level 7-10, where I most likely have most of my item slots filled with basic weapon damage and hp/mp items and a decent level of maim to be able to chase down and slaughter any demigod that overextends themselves.

Later I get the Mageslayer and that 4x crit sword that costs 18k, for a final end up at level 15-16ish of .7s firing rate with about 520-570 in base damage. Getting this expensive stuff relies heavily on me being able to lure out enemy demigods and then chase them down with DV and Maim purely dps wise rather than putting points in Snipe. The build has some real trouble early game though.