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 important factor in considering which sheets to buy is the weave of the fabric. Most woven materials (percale, damask, sateen, twill, flannel) will bunch and shift on a 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.
One more piece to consider is the way the seams are sewn in the corners of your fitted sheets. Sheets sewn with a "mitered corner" (found in many high end sheets) will be the most limiting when it comes to fit. The miters restrict the sheets to a certain height limit because of the way they are sewn, and may be more difficult to size and adjust accurately. Straight seam corner construction, however, provides more wiggle room for tucking the sheets under your mattress and keeping the fit of your sheets smooth and taut. The only thing I'm not certain about is whether or not you can tell what kind of corner construction the sheets have, without taking them out of the package.