Experimental Enchantments

Well, it would certainly help if we got some information of already existing magical items

but to start, Gloves of magic missile / eldritch blast.
basically a set of leather gloves with a crystal in the palm that fired magical blasts.

Yea, I suppose it would. In the empire, most magical items are sold to the aristocracy for self-defense or convenience: rings of life saving, cloaks of feather fall, boots of teleport, magic protection shirts, locks that (when locked) emit a deafening sound if an attempt to pick it is made, things like that. I've got a table I roll on for magical items in shops in the capital, but it's a bit complicated: Shop Table.

The Blasting Gloves are certainly doable, and they would be a good excuse for the emperor to accuse him of "the creation and possession of treasonous enchantments." 

Almarian, still plenty of time. The campaign is something someone asked me to do for a birthday in September, but since I won't have much prep time between sessions, I'm trying to flesh things out well ahead of time. Plus, since it's a birthday surprise, I'm making all of the characters and I want them to be well fleshed out. The more ideas the better, since I'm thinking about writing up his grandfather's enchanting journal as an in game artifact and will need to fill that with ideas as well.

Here's a few I've thought of in the last little while:
Goggles of Arcane Sight: Goggles that allow the wearer to see magical auras.
Arrow Catch: Think Kvothe's "Bloodless" but using chaotic bursts of energy to knock arrows down.
Clothing Washer: A container that creates water then agitates it in order to wash clothes (detergent not included).

Edit: I'm curious what the hat would do if it increased intelligence, but not stat-wise. Do mean no extra spell slots, but better skill checks? Or just the DM gives him more hints for being intelligent?

I love the candlestick, especially because it has a very logical enchant implementation in my magic/enchanting system. Enchantments that do illusions are hard under my system, but still doable, I think. Thanks for the great ideas!

I love it! Clothes of Self-Cleaning would be so useful at aristocratic functions.
The music box is great too. Not much music in the empire, but perhaps someone went and recorded some music in the South. That would be a status indicator!
I think a couple enchants working in tandem could do something cool with the limited area gloves with a little more strength than everywhere gloves of the same power level. That's a great idea!

Thanks for all of the great ideas guys! It's coming together in my head now. Here's what I'm think for the character's research items:

Arrow Blocking Pendant-Knocks down a certain number of arrows every certain amount of time within a certain range (I haven't worked out details).
Star-light Candlestick-The way magic works in my game, it is really convenient to make a spackling of little lights that get brighter as the environment gets darker. This is the thousands of lightning bugs concept.
Washing Tub-The tub automatically creates water and agitates it to wash clothes, not sure how often it will be able to activate.
Mine Overseer-Increases the Strength of people nearby
, like Frohtastic suggested but with a single minecart or hopefully something larger that increases miner strength and/or maybe constitution in the area to allow workers to do more.
Assayer’s Goggles-Arcane sight
for the wearer, intended to allow laymen to appraise magical items.
Fog Generator-A medium sized statue (not sure of what) that emits fogs from its mouth. Great for making private tables at an outdoor party more private and keeping things cool on during summer parties.
Rain Caller-A very large enchant, maybe a statue, but probably something made of wood, like a windmill or something, enchanted to put water into the atmosphere inducing greater rainfall in the area.
Music Box-A box that can record a single song with high audio quality. This one has a famous folk song on it from the Southern kingdom.

He's still got one slot left that I haven't decided on, but still plenty of time.

Meanwhile, his grandfather's journal will contain some of the work he did including self-cleaning and/or self-repairing clothes, youth pendants (which make the wearer look younger), dazzling hats (which increase charisma inherently, but also put on a light show), and after this he had enough experience to have some control over whether his enchantments were intelligent and started making intelligent enchants in the form of bookends and paper weights.

What powers would be useful for these desk items to have? Sure, them being smart and providing someone to chat with and bounce ideas off of is nice, but that's a side effect, what kinds of things would be good as the actual enchantment?

Never-melting ice, perfect to cool down your drinks or keep the pantry from perishing too fast.
Miners Lung, a breathing apparatus that cleans the air that the miner breathes in, no more sudden stops due to buildups of toxins.

How about an intelligent mood ring that always guesses the players mood incorrectly.
For office supplies, an intelligent paper shredded would be both strange and a little horrifying. As for light sources you could have an intelligent candle that never burned down.

I think a mimic that eats paper would be a fantastic shredder. The self writing quill could be a great replacement for a stenographer, and hilariously frustrating at other times, or simply has multiple settings. Goggles that make it seems as if there is ample light, but only to the wearer so as not to disturb other people. Magnetic bracers so that someone working can keep their tools in easy reach, and maybe it could even slide the right tool into place. Great ideas from everyone and a really cool concept!