One spell only
A spell storing weapon allows a spellcaster to store a single targeted spell of up to 3rd level in the weapon.
A spellcaster can cast any spells into the ring, so long as the total spell levels do not add up to more than three.
A spell storing weapon can only hold a single spell, so if you want to store three 1st level spells, you need three sets of armor spikes. This gets worse if you want to store a dozen spells, since there's only so many slots for spell storing weapons - gauntlets, armor spikes, perhaps your shield, and probably some weaponizable boots and hats from some source book. A ring, meanwhile, holds any three 1st level spells, at 3/4 the price of 3 +1 Spell Storing weapons. On the other hand, you can still use a Spell Storing Gauntlet multiple times at the start of the day for long Range: Self buff spells, punching yourself and then asking the wizard to cast into it again.
Damage adds up
Say you want to cast three spells at the start of the day, and then one in each of three combats: six attacks from your +1 Spell Storing Gauntlet. That's 6d2+6 times your strength mod. Perhaps 21 damage - or, at 10th level, about as much health as the 16,000 gp +4 Amulet of Health grants. On the other hand, healing is cheap. That's only 4 casts from a Wand of Cure Light Wounds, or 60 gold each day.
What if you miss?
Granting that you can hit yourself, you might have trouble doing so in combat. Unless your attack bonus is far beyond your AC, you have a decent chance to miss when trying to speed-apply spells. Try to sweet-talk your DM into automatically hitting yourself without a roll.
Arcane Spell Failure!
As far as I can tell, Arcane Spell Failure Chance applies to Spell Storing weapons. I'm not sure anyone has ever played it that way, or that anyone ever will, but if you're wearing plate armor and a heavy shield you have a 50% chance to fail to cast any arcane spell stored in your +1 Spell Storing Gauntlet. The Ring of Spell Storing specifically notes that it has no Arcane Spell Failure Chance, because it requires no somatic components, but I think that the Spell Storing weapon property... technically does.
Summary: Sure, sounds good
This looks like a fairly viable method. Using it in combat is a terrible idea because it takes an entire action, of course, though if your DM says you automatically hit you can use your last iterative attack on it. As long as you have your wizard around, you can use the Spell Storing weapon to cast Range: Self spells at the cost of a little damage, and before a combat you can punch yourself for a buff while the wizard casts his own buffs. It's certainly cheaper. With enough points in UMD, wands might be cheaper for 1st level spell application, and they save the poor wizard's 1st level spell slots.
Addendum: I hear some people think Shuriken can have Melee Weapon special abilities, and they are priced as ranged ammunition, so you could theoretically get 50 +1 Spell Storing Shuriken for 8000 gp, have your cleric store a bunch of buff or healing spells in them between adventures, and go to town. I'm not sure this works, mostly because the description of shuriken says
Although they are thrown weapons, shuriken are treated as ammunition for the purposes of drawing them, crafting masterwork or otherwise special versions of them and what happens to them after they are thrown.
I suspect that "otherwise special versions" includes special weapon abilities, so you can make a +1 Distance Shuriken but not a +1 Spell Storing Shuriken. I may be wrong. Obviously if your DM says that Spell Storing shuriken are legal, they are far cheaper than Rings of Spell Storing, and save spell slots as well as wands do.