There are many ways to do solo PvP: Corrupted Dungeons, Mists, Avalonian Roads, even the depths... Ultimately, in any area of the open world of Albion.
Take informations
Before attacking your opponent, view their equipment using the default keyboard shortcut (Y).
Avoid 1vsX fights: dishonor and shame could come far too soon.
Don't take expensive equipment into lethal zones, the risk of losing it can be high depending on where you go.
While still in a lethal zone, prioritize equipment and consumables that maximize your chances of escape.