Lowest Cost Vendor

Perhaps this is the wrong thread to post my question in, but I have been browsing for some time and decided on this one.

Sheet is set up like this:
COLUMN A
Product 1
...
Product 17

COLUMN B-D
ROW 1 - Vendor Name
ROW 2-17 - Price

Initially I had conditional formatting set up to highlight cells with MIN value PER ROW. Now I learned I can set up a formula that will take my selection of cells to discern CHEAPEST TOTAL PRICE (but needs to be by a single vendor), and even that I can have the vendor name pop-up by using the INDEX function.

SO, I want to know how to build an "open" formula (or macro) that will allow me to select which PRODUCTS I want to order in that shipment, and then which VENDOR to order it from based solely on CHEAPEST TOTAL (Vendor A offers p1 for $14, p3 for $2 and p14 for $10 - though these may not be cheapest PER ITEM, they combine to beat total price for all three items together).

Is there a way where I can have Excel prompt me to select which products I want to order and then calculate my MIN PRICE? If not, I will just adjust the formula everytime for the individual products, but I need to see the vendor name and total order value in my completed cell, but again, I really need the sheet to compute which total order value is least expensive [ in my mind it looks like this (excuse the formatting, not very good at this) =MIN(A1:D1+A3:D3+A14:D14 [ only if all three products come from same vendor]) and as you have just seen, I don't have the slightest idea with how to begin writing this formula.

Thank you, if I was not clear, please ask for clarification.