Your starting equipment is your equipment you start with at first level. Gaining a level in another class adds no additional equipment.
Player's Handbook errata clarifies this:
Class Features (p. 164). You gain the starting equipment of your first class only
Another question might be that a level 10 character should have more advanced equipment than a starting one, which is intended to be used by level 1 characters. That's covered in the question http://rpg.stackexchange.com/questions/69105/whats-the-starting-wealth-for-higher-levelsWhat's the starting wealth for higher levels?