Can a unit with ambush be played to base or does it have to be at a battlefield with a friendly unit?

You can play a unit with Ambush to your base at any time you could normally play a unit (during your Main Phase, in an Open State).

According to RiftJudge FAQ #10089:

• You can always play an Ambush unit to your base, but only at normal [Action] timing.
• The [Reaction] timing and the ability to play to a battlefield are conditional; they only apply when playing the unit to a battlefield where you already control units.

In summary, Ambush does not restrict you from playing the unit to your base; rather, it gives you the additional option to play it to a battlefield where you already have a presence, using [Reaction] timing.