Let's explore the wobble a bit more.
So, you spin the wheel. Is it the rim which seems to snake from side to side as it spins, or just the tyre? How much movement is there?
If it's less than a millimetre or so, it's not likely to be a serious problem. But it can be fixed by truing the wheel. The fact that you're asking suggests you should probably seek professional or experienced advice for doing that.
If the bearing is a bit loose, you won't generally notice this in spinning the wheel. But if you hold the wheel lightly at the rim and jiggle it side to siderelative to the fork, can you feel it moving but coming to a definite stop? If so, then, yes, there's a little slack in the bearing. Again, this is trivial to fix, but probably best done by someone who knows how, or under that person's tutelage (hey, that's a good word!)
But neither of these things is usually the cause of a judder. Juddering is more likely to be due to loose headset bearings or loose brakes. Hold the bike as if you were wheeling it, and put the front brake on. Jiggle the bike forward against the brakes and back. Can you feel a looseness there? If so, watch carefully as you jiggle it back and forth. What's moving? Can you see the fork wiggling relative to the main part of the frame? If so: head bearings. Or are the brake arms wiggling relative to the fork? If so, loose brakes.
Tightening either is trivial and this time, you can probably see to it with reference to Sheldon Brown or Park Tool websites or videos.
It might be none of those things. A mild judder or squeal can just be down to the combination of brakes, rims, brake blocks and the state of cleanliness of all of those. Greasy rims can cause juddering and squealing as the blocks grip, slip and grip again rapidly. Cleaning them thoroughly may help.
Same with brake blocks; sometimes lightly filing the surfaces or just changing them for new ones may help. Sometimes they wear unevenly and replacement or filing the faces flat does the trick. Sometimes, it's just an unlucky combination of slghtly flexy brake arms and forks and really sticky brake blocks; changing to harder blocks may help.