I'm quite an amateur at this kind of thing, but was going to hand embroider my grandmother's name on a piece of cottton, (then sew and stuff that to make a lavender bag).
My question is, do I need some sort of backing for the cotton I am going to embroider on? It is not particularly thin cotton, but I am concerned it might pucker or ruche if I embroider her name directly on to it. I was going to use chain stitch. Any advice gratefully received!
Embroidery does not normally need a backing fabric unless you are stitching on something stretchy such as t-shirt fabric, Kirsty. In that situation an iron on stiffener can be used while you are stitching and then trimmed around the design afterwards.
If you are wanting to make your work into a lavender bag then you would not want to use a very open weave fabric or else the lavender could escape! However, you wouldn't want to use something too thick either, or you wouldn't be able to smell the lavender through it.
I recently wrote a page about embroidering names which may be of help to you. You will find it here...
Embroidering a name
To prevent the fabric from puckering I would normally suggest using an embroidery hoop to keep the fabric taut. However, if you are doing chain stitch this would mean you have to work using a "stab stitch" technique rather than pushing the needle in and out of the fabric in one movement, as the hoop would make the latter more difficult.
Another stitch you could use, that gives a similar appearance to chain stitch, is split stitch. For this you would find a hoop very helpful. This stitch is also demonstrated on the embroidering names page I linked to above.
If you have any further questions please do not hesitate to ask.