Hi, I just wanted to share with you my favorite out-of-combat build that doesn't require active skills or potions. If this extremely obvious to you, my apologies, please move on. This build will require a stamina-centered character for long periods of sprinting. Specific to the sneaking, it works best with a Khajit or Bosmer Nightblade but it's not necessary.
All we need are four sets: Jailbreaker, Night's Silence, Night Terror and Might Mother's Embrace. These are all medium, and preferably well-fitted (not much difference for the last two).
The key is how we assign the pieces to make them flexible.
For the speed build, use any 5 pieces of Jailbreaker armor plus Night's Silence swift jewelry and 2 more pieces. You get 2 open slots; I chose to leave the weapons free so I can use my main battle weapons in a pinch. If I've done my math right you'll get minimum of 34% speed boost at all times from swift (blue quality) and Jailbreaker, up to 45% with gold jewelry and The Steed. You can still use Major Expedition if you like. While sprinting, apply the 40% sprint bonus plus 21% from a 7-piece medium armor passive and you get 95% to 100% boost (hit the cap with gear alone). As an added bonus, you can sneak without losing speed!

Now for the crime build, we'll include that Night's Silence jewelry plus one armor piece and a weapon swap. We'll use one weapon swap for either Night Terror or Night Mother's Embrace, and fill the remaining armor slots to form a 3-piece of Night Terror and a 5-piece of Night Mother's Embrace. Now on one hand, we have a fairly sneaky build that can move at normal speed (enhanced by that swift jewelry and possibly Concealed Weapon). Swap to the other hand for the extra sneak radius when you're in a tight spot. (You may need to become visible and hide again for the change to take effect, due to a game glitch.)

Let me know of this was helpful and how you think it stacks up with other techniques.