I bought that exact same bag for my sister and before I gave it to her I put it in a pillow case and washed it in my washing machine on gentle cycle, warm water. Not all of the stains came out, especially the darker ones, but the bag itself came out beautifully! The sequins all survived. This was maybe 5 years ago and that purse is still her daily carry bag. She says she loves it. If she only knew what it looked like before the bath.....
Out of your cleaning stuff I would probably bath it in warm water and dawn, gently scrubbing any dirty areas with an old toothbrush. Then rinse. I haven't washed that bag but a similar cloth one with sequins and they all survived fine. I'd probably only resort to the washing machine if it was really really filthy.
I've used Soilove on a bag with similar material. It worked great. I think I scrubbed it with a brush then rinsed it really well.
I used ALL of the suggestions lol. I started with some Shout in the bad parts, I was able to make a bad ink or something stain on the bottom better. Then I gave her a bath with dawn for 20 min, quite traumatic for me, I felt like I was killing her. She gurgled and everything




ETA: Once she's totally dry, I'll post the before and after and see if you guys can see a difference. DD thinks I've just been looking at it for too long. Lol