I have embroidered on just about everything except Balsa Wood ( not game for that) and I have found that sometimes dressmakers interfacing works the best for some things. Not the iron on type and a new sharp needle.
Are you making the item from scratch? or is it ready made?
If possible do a test with fabric interfacing and the most dense part of the design to see how it goes.
I am sure more advice will follow.

I have used this fabric before...I usually do not wash my fabric...but for those who do...please go ahead and do so...I "stabilize" this fabric with "goo" that is made from WSS scraps...water and WSS scraps..dunk fabric to saturate...spread out flat and let dry...lightly iron with a press cloth...the fabric should be stiff...embroider...this works well with various light weight fabrics that have a tenancy to pucker...If you don't want to go the 'goop' route...spray starch heavily several times until the fabric is very stiff...then embroider...not sure what kind of design you are planning to use, but on a fabric like this it is best to use a lighter density design...

I am not expert enough to try to guide you through this process but I see that you have already had some good advice. There are a number of embroidery websites that offer guidance blogs on all manner of potential embroidery problems, one of which is Embroidery Library. I have, hopefully, added the links to two sources of information which in any event are always worth reading. Hope that this helps.

Kim's advice about the goo seems good to me, but most important is to not try to use a dense design. That is asking for trouble.

I use liquid goo for any drapey fabric. Velveteen do loosen up with handling, however it is enough to get the job done. Good Luck

Sometimes having a too high a tension on the threads results in puckers. If you puckers on other types of fabrics you sew, the tension is probably ok. Some fabrics just pucker for me even if I starch the fabric stiff.

In that case, I stablilize the fabric on the back with washaway stabilizer using temporary spray glue. The I lay 3 layers of washaway stbilizer on top. Do not use spray glue for the top. Just lay the stabilizer on top. You don't want to use spray temporary glue on the top stabilizers because that will make the layers too difficult for the needle to get through and you can break a needle.That little extra space that the washaway puts in there helps get rid of puckers.

I often use leftover pieces of stabilizer when doing this. This can result in the sewing machine's foot getting caught if it should slide under the loose stabilizer on top. So I usually just use scraps for the first two top layers, then a larger top piece to lay on top to prevent the foot from getting under the smaller stabilizer pieces.

I think I conquered it. I starched it a lot and used 2 layers of tear away underneath.
Now I just have to conquer satin. One design on the satin worked great with just 2 layers of tear away underneath but my lettering is puckered.