I assume from your profile you're a low hours student - so am I, but a bit further on.
One of the things you'll probabably need to do before going solo will be the air law exam and for this you need to learn the minimum visibility requirements, amongst loads of other stuff. There's a very confusing looking diagram in Thom book 2 if that's what you're using. I found this stuff took ages to remember so I'd start to learn it as soon as possible.
Having said that, I still get it wrong and can't really judge the suitibility of the weather properly yet. I'm assured it gets easier with experience, and it's not my decision at the moment, so that's OK.
As the others say, haze is bad because it looks such a damn nice day from on the ground. The problem can be 'slant visibility'. Just because you can see the ground 1000ft below you, doesn't mean you'll be able to see the airfield which may be only a mile to one side and therefore over 4000ft away!
At times I'm surprised at how bad the weather has to be before we can't fly. In the first few hours we often cancelled because learning the basic skills in bad weather can be difficult and counter productive, but now they're quite happy to let me solo in the circuit in rain and under a 1000ft cloudbase so long as the wind isn't too bad.
The minimum requirement is that I must be clear of cloud, in sight of the ground, and have at least 3km visibility although I think it's 5km under most circumstances, not sure. See, I told you it was confusing.
As for wind. Each aircraft type has a crosswind limit for take off and landing. Mine is 12kts. So it depends on wind direction as well as speed. When looking at forecasts, dont forget that the winds at altitude are often stronger and in a different direction to those on the ground. Again, clubs will also have their own rules on what students can and can't do alone.