1.   Best value is the result of trading off multiple desired attributes of a complex purchase and there is not enough budget money to buy them all or no one design can deliver them all.  The best value is the one that delivers the most value for the least cost.  It is normally a highly subjective decision because it is not normally possible to mathematically rank or compare the attributes that have to be traded.  A decision matrix is often used to try to put the attributes into some sort of mathematical order -- although best practice is to use it as a method of illumination rather than for the actual decision.  As an example, if there are 5 requirements (a, b, c, d, e) and there are 3 vendors.  Each vendor has a solution that meets some, but not all of the requirements. 
2.   a, b, c, e - $1.0 M
3.   b, c, d, e - $0.9 M
4.   a, d, e - $1.1 M

The decision maker then has to decide which solution results in the best value for the government.  It could be based on a lot of external information.  Maybe "d" can be purchased later as an add-on.  Maybe "b" is an absolute "must have".  Maybe "c" is really more important than "d" and "e" combined.  All of that has to be balanced and decided on in order to reach a decision.

1.   There is no best cost estimating method.  A vendor quote for a commercial-off-the-shelf purchase is likely to be the most accurate, but it may come at the expense of costing time to get the quote.  It also is only appropriate in a limited number of circumstances.  The "best" one to use is the one that gets to a reasonable answer for the kind of question being analyzed given the available time to come up with the answer, the historical data available, the skill of the estimator, the quality of the description of the item to be estimated, and the estimating tools available. Big DoD decisions usually have enough time and many people to work on it, but it might be so large and complex that it requires every method in some measure.  If the complex problem is broken up into many pieces, each piece may have its own preferred method because each piece may have its own historical data and quality of the item description. However, if someone is looking for an order of magnitude estimate and they need it in 2 hours, then that is going to seriously limit the method that can be used.  The preferred method always ends up being the one that answers the mail.