Creating a GUI data calculator, running functions with multiple criteria

Hi all,

With some minor experience with vba, I am still pretty new to excel, but a quick learner! Please keep that in mind as you read on.

I have a bunch of data in a spreadsheet, and so far I've been able to create a user form to add entries to this data.

Now, the next thing I want to do is create a GUI that filters and calculates the data in numerous different ways.

This is a screenshot of what some of the data looks like:
Image 1
Screen Shot 2015-04-18 at 4.18.46 PM.png

Here's a summary of the types of calculations I want to do and the criteria that would follow:
Image 2
Screen Shot 2015-04-18 at 4.20.05 PM.png

I want to be able to have a GUI where I can check a bunch of criteria, then choose a calculation method to run on the data under that criteria. Here are some examples for clarification:

Example 1: Calculate the average of how much the 20lb washer brings in.

Example 2: Calculate the average of how much the 20lb washer brings in on Saturdays.

Example 3: Calculate the average of how much the 20lb washer brings in on Saturdays, when the weather conditions are "Sunny".

Example 4: Calculate the average of how much the 20lb, 30lb, and 40lb washer bring in on Saturdays and Sundays, when the weather conditions are "Rain" or "Snow".

In other words, when looking at the summary of calculations/criteria image (Image 2) imagine a checkbox next to each criteria, so that ideally you can run any calculation using any criteria (no matter how many).

I understand this is probably a pretty big task, so I'm not asking anyone to spell out the entire process. Rather, I would appreciate any/all suggestions/tips/related posts/tutorials/methods of implementing this.

Note: I have tried using the AVERAGEIFS function...the issue is once you start piling up the criteria, you need an awful lot of functions...

I want to be able to run these calculations at any time, with any criteria (which is why I was thinking of a GUI).

ALL GUIDANCE IS MUCH APPRECIATED

Thanks in advance!!

Edit:
Attached is a sample mock-up of the data and the four example calculations.
ForumExample.xlsx