Aviation minimums

no thunderstorms. only clear skies and fog(since you will fly above the fog)

do not know about the rules applicable in ur country, but generally for a first solo cross country flight l would like my potential students to have 3NM visibility, & no clouds below 5000ft.
the more experienced the worse conditions, down to our local VFR minima which is 2.5 km visibility /for fixed wing/ & 1500ft AGL cloud layer for daytime operations.

flying ABOVE fog might be considered VFR in US, but still it requires more or less IFR equipped plane & l would be strongly against beginner pilots being encouraged to fly in such conditions.

l am presuming that u r in the US & thus flowing the FAA rules.
According to FAR 61.87 a solo student has to abide by the airspace rules & procedures for the airport where the solo flight will be performed. Also, according to FAR 61.89 a solo student may not fly a flight with surface visibility of less than 3 statute miles during daylight hours or 5 statute miles at night. Also according to FAR 61.93, reviewed the current & forecast weather conditions & has determined that the flight can be completed under VFR.
Those rules r the absolute minimum of course. But l would agree with the past contributors. You want to be at least 5,000 feet ceiling (clear of cloud) & 5 mile visibility. You really do not want to fly solo in a light single even in a MVFR. Trust me, experimenting u piloting & navigational skills in an inclement weather is never FUN.
KEEP ‘EM FLYIN’

3 miles visibility and legal cloud separation requirements OR whatever restrictions your instructor has put on your medical. l always used to limit my students to 5nm visibility, 5000' ceilings and no more than 5 knots of crosswind component.

Depends on what licenses or ratings you hold. As a stucent working on your PPL, standard ''day VFR''. some flight schools have higher minimums for students to fly their planes sols (which they are allowed to set), but ''day VFR'' is the FAA is legal minimum weather requirement for student pilots to solo.