How tight should my spokes be?
For your wheel to stay ‘true’ and not develop a wobble, your spokes should be nice and tight and even all round. This is something you can keep an eye on yourself at home with the use of a spoke key.
Any spoke that is tighter than the rest may cause the ones next to it to loosen, and is more likely to snap as it’s taking more strain than it should do. Loose spokes aren't pulling their weight and will cause the rim to develop a buckle.
If the spokes are too tight though, you risk damaging the spoke eyelet of the rim.
Keep in mind that it is normal for new wheels to come out of true during the initial few weeks of riding as the spokes bed into the hub. This is another reason you should book your bike in for that free first service as things like this will be addressed and set your bike up for years of faithful service.
Anything more than a minor true should really be addressed by an experienced bicycle mechanic.