My professional opinion is don't spray it. There are a couple of options as to your paints.
If you have a Michael's near you, they sell little tubes of no-prep metal paint. Some stores stock them in the section where they have model cars. Those are water-based.
If you can't find them, get a can of Krylon (or whatever brand is appropriate for metal), carefully spray that into a cup (I just use the cap) and brush it onto the fixture that way. If you get them at Michael's (or similar arts/crafts store they're available in small cans).
Pick up a couple of artist's brushes, and some blue tape, too.
HD sells little cans of Rustoleum, which will also work.
You can use an acrylic since the fixture won't be touched. If you do that, don't put it on too thick.
I'm fairly certain you can't remove the glass (although yours may be different).
Gently stroke the paint on, avoiding that flatness. First do the black, then the brown, exactly as you described it.
Take the fixture down to paint, if it's up. And, since you have some space between the metal and the glass, slip a piece of paper underneath while you're working instead of tape. The tape may get stuck in places and don't risk breaking the glass.

I'm sure paintergirl knows more about this than me. But I just wanted to let you know I painted a chandelier (taped off the electrical parts and the "candle" parts. I used a spray paint that is "oil rubbed bronze" color. It was great because it gave a variation of color. Also the hammered metal finishes might do the same thing. So if you want to go forth with the spray paint, look for those type of paints at Lowes or HD. I agree you don't want it to have a "uniform" finish.

I just didn't think spray was good with glass. And it also appears that the fixture in the picture has more of a brushed finish, less textural.
But I do agree that those sprays are awesome. I've probably used all of them at least once, lol!!

I recently did 3 light fixtures with glass and tried 2 diff ways. The first was to use tape and the second, no tape but a sheet of paper to mask. The tape was tricky to pull up in a few places. Where it wedged way under the glass, it tore and was difficult to pull out. Cleaning the paint off the glass wasn't that easy, either. I did need a razor, but so afraid of scratching the glass.

So, I like to share my knowledge, or more specifically, my mistakes with others. In return, I get to learn things, too!

Oh yes, I agree about the glass issue! The chandy I painted did not have any glass. Like I said, I am sure Paintergirl knows much more than I do regarding painting. Much more.

I have spray painted many light fixtures. My onion lamps on the outside my house were the same bronze color. I had 10 of them and it would of been to much money to change them so i took the glass out and painted them. That was 4 years ago. They still look great. I would do it again. Good Luck

Thanks everyone for the great advice. I will post results later this week. Wish me luck :-)

Well, here is the end result. It's exactly what I wanted. I ended up using regular flat black all purpose metal/wood spray paint becuase we had some and my Michaels did not have the tube metal paint. I slipped paper to cover the glass and brushed it on lightly. I let a hint of brown show through in places as I dont think I am going to tackle the interior- mostly becuase I cannot even figure out how to open the light fixture and my husband is out of town!

Befre:
{{!gwi}}

After:
{{!gwi}}

Thanks to paintergirl and everyone for their advice!

They look awesome! And yeah, they don't make it easy for you to remove that glass to get inside!! Guessing because they want you to buy another? Huh, you showed them!! :)