Generally speaking, the weather minimums for a student pilot will be something that is discussed and agreed upon between students and their flight instructor. However, for student pilots flying VFR, it is widely accepted that the weather minimums are 3 miles visibility 500 feet below, 1000 feet above, and 2000 feet across. In addition to this, there are also weather minimums imposed for the crosswind. These are usually very strict for student pilots who are just starting out, and the flight instructor will usually give a limit somewhere around the vicinity of 20 degrees of runway heading that is less than 10 knots. However, as the student progresses and gains experience, these limits are usually relaxed somewhat.
As for flying solo, the weather minimums will greatly depend on the circumstances. If you are going to be taking the aircraft out completely alone, then the weather minimums will be discussed and agreed upon with your flight instructor before the flight takes place, so that you are completely prepared. For safety, the weather minimums are usually quite strict for these types of solo flights.
In contrast, if your flight instructor is going to be on board, then your flight instructor may choose to relax the limits in order to provide you with a challenge. These types of solo flights will grant you more freedom, as the presence of your instructor will serve as peace of mind that you are not alone, which will give you the confidence to experience flying an aircraft with different minimums than you’re used to.