Boo,
You stated you looked all over, but considering that much of your question forms the basis for 14 CFR 121, I have to question how far you looked. Did you look at the FAR? I've included some (emphasise only some) of the relevant regulations, in part, below. There is a lot of information that is applicable to weather a flight may be released, or dispatched, for weather, fuel, and other considerations. The following is only part.
To emphasise how much material you need to cover, the reply is broken down into three parts here. The response you received previously by chperpilot is correct; if you're starting on your flight training, you need to concentrate on that, not this. There is no way you can effectively learn your elementary flight protocol and become involved in preparing for 121 at this stage, effectively.
Any school or instructor that would expect you to be studying for this material right now, at this stage in your training is putting the cart before the horse, in a very irresponsible manner.
Destination weather under 14 CFR Part 121 may is subject to the following subparagraphs (butchered in part for brevity):
121.195(d): "...no person may takeoff a turbojet powered airplane when the appropriate weather reports and forecasts, or a combination thereof, indicate that the runways at the destination airport may be wet or slippery at the estimated time of arrival unless the effective runway length at the destination airport is at least 115 percent of the runway length required under paragraph (b) of this section."
121.567: "No person may make an instrument approach at an airport except in accordance with IFR weather minimums and instrument approach procedures set forth in the certificate holder's operations specifications."
121.599(a) & (b): "No aircraft dispatcher may release a flight unless he is thoroughly familiar with reported and forecast weather conditions on the route to be flown. No pilot in command may begin a flight unless he is thoroughly familiar with reported and forecast weather conditions on the route to be flown."
121.601(b) & (c): "Before beginning a flight, the aircraft dispatcher shall provide the pilot in command with all available weather reports and forecasts of weather phenomena that may affect the safety of flight, including adverse weather phenomena, such as clear air turbulence, thunderstorms, and low altitude windshear, for each route to be flown and each airport to be used. During a flight, the aircraft dispatcher shall provide the pilot in command any additional available information of meteorological conditions that may affect the safety of the flight."
121.611: "No person may dispatch or release an aircraft for VFR operation unless the ceiling and visibility enroute, as indicated by available weather reports or forecasts, or any combination thereof, are and will remain at or above applicable VFR minimums until the aircraft arrives at the airport or airports specified in the dispatch or flight release."
121.613: "No person may dispatch or release an aircraft for operations under IFR or over the top, unless appropriate weather reports ( & forecasts, etc)indicate that the weather conditions will be at or above the authorized minimums at the estimated time of arrival at the airport or airports to which dispatched or released."
121.615(a): "No person may dispatch or release an aircraft for a flight that involves extended overwater operation unless appropriate weather reports or forecasts indicate that the weather conditions will be at or above the authorized minimums at the estimated time of arrival at any airport to which dispatched or released or to any required alternate airport."
121.631(b): "No person may allow a flight to continue to an airport to which it has been dispatched or released unless the weather conditions at an alternate airport that was specified in the dispatch or flight release are forecast to be at or above the alternate minimums specified in the operations specifications for that airport at the time the aircraft would arrive at the alternate airport. However, the dispatch or flight release may be amended enroute to include any alternate airport that is within the fuel range of the aircraft."
121.637: "No pilot may takeoff an airplane from an airport that is not listed in the operations specifications unless -(Airports in the United States) The weather minimums for takeoff prescribed in Part 97 of this chapter; or where minimums are not prescribed for the airport, 800 - 2, 900 - 1 1/2, or 1,000 - 1.
Airports outside the United States. The weather minimums for takeoff prescribed or approved by the government of the country in which the airport is located; or where minimums are not prescribed or approved for the airport, 800 - 2, 900 - 1 1/2, or 1,000 - 1."
121.649: "Except as provided in paragraph (b) of this section, regardless of any clearance from ATC, no pilot may takeoff or land an airplane under VFR when the reported ceiling or visibility is less than the following: for day operations - 1,000 foot ceiling and one mile visibility. (2 miles for night).
Where a local surface restriction to visibility exists (e.g., smoke, dust, blowing snow or sand) the visibility for day and night operations may be reduced to 1/2 mile, if all turns after takeoff and prior to landing, and all flight beyond one mile from the airport boundary can be accomplished above or outside the area of local surface visibility restriction.
The weather minimums in this section do not apply to the VFR operation of fixed wing aircraft at any of the locations where the special weather minimums of § 91.157 of this chapter are not applicable. The basic VFR weather minimums of § 91.155 of this chapter apply at those locations."
121.651: "No pilot may begin a takeoff in an airplane under IFR when the weather conditions reported by the U.S. National Weather Service, a source approved by that Service, or a source approved by the Administrator, are less than those specified in the certificate holder's operations specifications; or Parts 91 and 97, if the certificate holder's operations specifications do not specify takeoff minimums for the airport."
