I'm really good at coming up with interesting (well, to me, at least - and I guess that's what matters) character concepts for long term campaigns. I suck a lot more at one shot types, particularly low level ones.

I've managed to find a FLGS that does (what's advertised as) weekly one shots. I went along with an old character to try it out, and enjoyed it. My impression is that while experimental single-session characters are welcome, the other players seem to use the same characters each time. Which is also fine. The quests themselves while linked together in the sense of the party is assumed to be the same (there was an introduction of "last time, we..."), there is no overall narrative. Just a bunch of guys earning beer money, as it were. A significant issue is that due to having young kids (precisely the wrong age for D&D with minis!), I won't be able to attend every week. Probably every two weeks.

The guidance was to create L3/4 character, I'm not sure if there is any progression though - no mention of XP (some where brand new players, so there couldn't be any expectation that they'd know the XP values) and no mention of leveling up, so it may well be an eternal L3 or L4 job.

So my request is, do you have any ideas on good concepts to try that would have time to shine in one-shot situations? The circumstances:

- L3 or L4.

- One shot.

- No restrictions on what sources I can use for my build. Would be nice if it leant itself joining the adventuring party, though.

- Current party seems to be (no subclasses known, I didn't hear or see anything to give it away): A Drow Paladin, Half Orc Barbarian and a Warlock (with a Quasit Familiar) based on Emporer Palpatine. I would like to be something different - I was a Warlock last time (I wasn't aware of the party makeup) and while we were able to avoid treading on each other's toes, it would be nice to be able to just run with the character without worrying about it.

- The DM likes his Intelligence checks. It was strange for me, who leans more heavily into Wisdom (particularly Perception and occasionally Insight), but everything was Intelligence. Eg I yelled for help because I was attacked while the party was split, so he had them do Int checks to see if they recognised what was happening. But yeah, he likes Int checks, although I don't consider that essential (if I fail them, it doesn't really bother me, especially if it's just the price I pay for having a cool character).

- It wasn't cut throat (we had one go unconscious and was never in real danger of dying), it's just a bit of relaxed fun, so it doesn't have to be super optimised at all.

- I'll use Point Buy and floating ASIs.

- Setting is Forgotten Realms, or at least the quest we did would have fit very well there.

- No starting magic items. He gave us a couple of healing potions for the party at the beginning of the quest, but he never mentioned anything about choosing magic items.

- I've played an Evocation Wizard before, so would like to avoid that. Others I've played, but haven't had chance to properly explore so I'm open to redoing them (including other Wizard subclasses).

Any suggestions?

Seems like a good time for artificer.  Inty class with decent checks, can manufacture its own magic swag at need.  Highly versatile, spell prep means it can flex whenever somebody new shows up. All subclasses not named Alchemist have something cool at third level. Would be where I'd start. 

Disclaimer, I am the last person you want to ask, as my characters always end up weird.

Stick, the Animated Scarecrow (Warforged Cleric: Twilight Domain, Gladiator Background)

ZimBrimble TurboBlaster (Deep Gnome Warlock: Genie, Archaeologist Background)

You could use it as a chance to play test one of the things everyone says is overpowered. Like, actually play a twilight cleric for a few sessions. If you don’t like it, swap to something else. 
Or try the PHB ranger and the Tasha ranger in back-to-back sessions and see the difference. 

A little MAD, but you could play an Inquisitive rogue.

Or maybe a bard?  Eloquence or Lore?

Go for the divination wizard halfling with the lucky feat. Tell the dice gods to eat your farts.

Twilight cleric that always casts Guidance or an artificer would be my choice.

I'm in a server that does regular one shots. I like to use it to play different builds I may think of, but I think the funnest for me are the gimmicky characters, like the Christmas one shot with the gnome artificer who wanted to be a toy maker or the 80s metal bard.

I built a goblin diviner wizard and it works quite well. Just get spells like absorb elements, silvery barbs, and shield, as well as the lucky feat if you start at L4, and someone's final roll is never really their final roll.

Silvery barbs works well with portent because you can force a reroll on an opponents check, and then dictate the result. Usually, you have to use portent before the roll, but by just expending one first level spell slot you can wait to see if the opponent passes and then expend portent. This doesn't work for allies since silvery barbs specifies that the target takes the lower roll, but it does work quite well when opponents attack.

This build is really designed to elevate your allies, and it relies heavily on reactions and off turn abilities, so it is quite complicated. But if you play it right, it works really well.

Just keep in mind that lucky and portent aren't reactions. When I played this, since I had so many reactions, I wrote down what each of them were. You can avoid taking damage because a goblins nimble escape lets you make good use of your action economy, and hide (or disengage) as a bonus action.

This works moderately well with your party, because it mostly plays support and helps stop the barb and paladin from taking a lot of damage. Though this is another spellcaster, it's built so differently from the typical D&D spellcaster that I don't really think they'd overlap a lot. This is also good since you said the DM makes you do a lot of intelligence checks, and that's the wizards spellcasting ability.

  If not this then a skill monkey such as artificer or rogue would probably be the second best option. Artificers are great and also need a high int score. And rogue's are always good if the party wants to sneak around or get through a locked door.

Ranger is a solid possibility- keep in mind that nature and investigation are intelligence based skills . Depending on background choices you should be able to get stealth, nature, investigation, survival and perception skills( or at least 4 of the 5) - just don’t dump stat intel. Maybe something like a  bugbear hunter.

I had already come up with an Artificer for another campaign that is...slow going, and he didn't get to shine (really small party and was hard pressed in fights). I'm going to run him for the next session, since I have an STL file for him already and the class came up several times in this thread. However, there.is plenty of room for these other ideas, all are pretty cool and a couple really caught my eye.

I really like the idea of a Goblin Gloomstalker, but it seems like actual darkness is very situational?