If a run is successful what can a runner access?

By BilliousBT, in Android: Netrunner The Card Game

Example 1: Runner sucessfully runs at HQ which has an installed upgrade.

Does the runner choose to access a random card in the corp's hand or the upgrade or can he access both?

i.e. On success does the runner access HQ or the HQ Core or both?

Example 2: Runner sucessfully runs at a secondary server which has an installed upgrade and an asset.

Does the runner have to opportunity to trash both or just one of them?

Both examples have the same answer.

The runner decides what order to reveal the cards. If you want to check the Upgrade on HQ first, go ahead, but you MUST decide what to do about that upgrade before you move on to the HQ draw. You can't see the upgrade, Pull the card from HQ, and then decide to trash the upgrade. Same goes for Remote servers. You look at all the cards installed, one at a time, decide what to do about each, then move on to the next.