How to 'pick' transactions to include when attempting to add a new block? I saw this question about finding new transactions.

But how do you pick which transactions to include in the block you're trying to add? Should it be in a certain order, or random? How many transactions should you include? Looking at the blockchain I've seen anywhere from just a few, to hundreds. Is the number of transactions something you'd vary when pool-mining to combat exhausting all possible nonces if up-to-date with the timestamp header? (Loosely related to my other recent questions).
Basically, you can include whichever transactions you'd like.

Currently most miners simply include all valid transactions they know of. It is cheap to do so.

There is currently a limit of 1 MB per block, so as transaction volume reaches these levels, miners will typically want to include transactions that have the best ratio of fee / data size.

As a more mature transaction fee framework evolves, miners will choose transactions to optimize for it.

Playing with transactions included is not needed to extend your work scope, as you can extend it indefinitely by changing the extraNonce.