We're getting off track. Discussions of safes with one million combinations is off-topic. The original poster has a requirement of quick access. A safe that meets the original requirements is not going to be high security. However, if someone can provide a link to such a safe, then please do.

If you don't want to go electric, then a Simplex lock is the way to go. I'll trade a little security for more reliability of Simplex locks. Inexpensive electronic locks just don't meet my standard for reliability.

If you still want to go electric, the Gunvault may meet the original criteria. However, I have experienced failures with this safe and have read numerous stories of Gunvaults failing (Google "Gunvault failure"). Do you want a safe that won't open if you fail to maintain it perfectly? Do you want a fun gadget that's less reliable than a Simplex? If yes and yes, then the Gunvault will be fine.

The wall safe linked above appears to be for mounting permanently in a wall and has limited mounting capabilities. I wouldn't want to go that direction for a small, quick access safe that I'll want to move around.