I think in most case it's used as a transitive verb.
「してやったり！」の表情を浮かべる:
His face shows "That's what I expected!"
不敵な笑みを浮かべる.
The dog's face shows fearless smile
I think you can use "浮かぶ” for more spontaneous/natural things.
彼女の顔から自然な笑みが浮かぶ。
Her face shows natural smile.
You can use it for holding an idea.
良いアイデアが浮かんだ。
I have hit on a good idea.
I think 思い浮かべる/思い浮かぶ is more of making a conscious effort.
鍵をどこに置いたか思い浮かべる。
I am trying to recall where I put my key.
昔、旅行した場所の風景を思い浮かべる。
I am remembering the scenery where I traveled before.
Edit1:
As for, It makes me think of home.
If you have an image of hometown, probably 故郷が思い浮かんだ。or something.
Probably having an image for a short period like,
If you forgot something at your home and you don't know where it is, but anyway you rush back home.
忘れ物が浮かんだから家に帰る。
I think I forgot something.Anyway I go back home.
Edit 2: My analysis of The difference between 浮かぶ and 思い浮かぶ.
I think 何かが浮かぶ is more of a flash thought. It just contains not necessarily so clear mental image such as "Oh, I was boiling water.I forgot it.I need to turn it off" It is more of an instantaneous thought. I mean it is used for miscellaneous thought.
On the other hand, I think 何かが思い浮かぶ is more of a clear thought, better resolution of the mental image. And it tends to associate with one particular concept. As you pick up "It makes me think of home" since you know what it is in detail.