Update from August 28:
Apparently, the topic of “fresh Classic servers” is slowly but surely becoming concrete! In an update post on the official website, the developers confirm that there will soon be good news for players who want a fresh start with WoW Classic. Here is the exact wording:

“We’re also working on a surprise for WoW Classic players who want a fresh start, and we’ll let you know about our plans soon.”

As soon as Blizzard reveals the concrete plans for “WoW Classic Fresh”, we will of course keep you updated.

Original message from June 25:
Before the launch of WoW: Burning Crusade Classic we asked Patrick Dawson and Holly Longdale in the course of an interview, what the plans are for the Classic era servers and fresh Classic servers. The answer in both cases: Blizzard first wants to get the launch of TBC Classic smoothly over the stage before they deal with these issues in detail.

Well, the launch is now a good three weeks ago and indeed the developers now seem to change the focus. Once again, a Classic survey has been sent out by Blizzard to selected WoW players to get their feedback on certain points (via Wowhead).

In the first question, Blizzard wants to know how likely you would be to start on a new Classic server if the following changes were implemented there:

• Summoning stones in front of all dungeon entrances
• More difficult raid and dungeon challenges
• Increased debuff cap on raid bosses
• Barbershop
• More experience points when leveling
• No world buffs in the raids

In a second question, the developers explain that they are thinking about bringing Classic phases online faster on fresh Classic servers. Which phase cycle would players prefer?

• The same phase cycle as in WoW (buy now ) Classic (21 to 22 months)
• A shortened phase cycle of 12 months, with a new “Fresh Start” every twelve months.
• A significantly shortened phase cycle of 6 months, with a new “Fresh Start” every six months.
• A different cycle (with text column to specify).

And the final question: how much do you like or dislike the following changes, with fresh Classic servers in mind?

• More experience points when leveling
• Barbershop
• No World Buffs in the Raids
• Increased debuff cap on raid bosses
• Black Market Auction House for Vanity Items
• More difficult raid and dungeon challenges
• The original Alterac Valley design (more guards, longer matches, additional quests).
• Increased drop chance for items
• You earn gold faster
• Summoning stones in front of all dungeon entrances