We don't have a specific brand or company to recommend, but we have some information for you that may be helpful as you go about making a decision about which sheets to buy for a Spindle.
When it comes to size, all sheets are not created equal. Just as in clothing, a Medium sized shirt varies widely between Land's End, LL Bean, Gap, etc. So it is with sheets. We recommend you look for sheets that fit mattresses up to 14" deep. Any more than that and it's likely you'll be dealing with extra fabric. But, one company's 14" fitted sheet may be loose and baggy where as another manufacturer's 14" fitted sheet may fit like a glove.
Another factor in considering which sheets to buy is the weave of the fabric. This is more a matter of personal preference than a matter of right and wrong. Keep in mind that woven materials (percale, damask, sateen, twill, flannel) may bunch and shift on some mattresses, but if you've always slept on these without any issues, feel free to continue to use them on our latex mattress. Sheets made of a knit fabric, most often cotton jersey, are stretchy and have less of a tendency to bunch and buckle. Cotton knit jersey will offer you a snug, smooth and comfortable feel, while staying anchored under the corners of your bed. If they have a little bit of stretch in them - like lycra or spandex - even better.