It is highly recommended that you read the books in the order they were published!

That way you avoid having some fun surprises spoiled.
You should definitely read Mossflower before The Long Patrol and Lord Brocktree, Salamandastron before Marlfox, Redwall before Taggerung and Mattimeo, and Mariel of Redwall before The Bellmaker.  In other words, you really are best off reading them in the publication order.

For anyone who is interested, I, Snowfur, read them in the publication order, except Redwall and Mossflower were flipped around, so Mossflower was the first book in the series I read.  Of course, at that time, Mattimeo was brand-new!  I feel so old...

The publication order of the Redwall books

• Redwall
• Mossflower
• Mattimeo
• Mariel of Redwall
• Salamandastron
• Martin the Warrior
• The Bellmaker
• Outcast of Redwall
• The Great Redwall Feast
• Pearls of Lutra
• The Long Patrol
• Marlfox
• Legend of Luke
• A Redwall Winter's Tale
• Lord Brocktree
• Taggerung
• Triss
• Loamhedge
• Rakkety Tam
• High Rhulain

 

• Lord Brocktree
• Legend of Luke - part 2
• Martin the Warrior
• Mossflower
• Legend of Luke - parts 1 and 3
• Outcast of Redwall
• Mariel of Redwall
• Martin the Warrior - framing sequences only
• The Bellmaker
• Salamandastron
• A Redwall Warrior's Tale (short story included with the Build Your Own Redwall Abbey kit)
• Redwall
• The Great Redwall Feast
• A Redwall Winter's Tale
• Mattimeo
• Pearls of Lutra
• The Long Patrol
• Marlfox
• Taggerung
• Triss
• Loamhedge
• Rakkety Tam
• High Rhulain