If the wood has no apparent varnish coat, use a low-VOC water-based primer as your first step. The principal advantage of this class of primer is that it bonds exceptionally well, and it is relatively odor free and pollutant free. Although these primers are usually supplied in white, you can select tintable varieties that approximate the color of your intended topcoat. Once the primer has dried, the wood's grain may be more apparent. Use grade #000 steel wool to smooth the surface, then apply a second coat of the primer.
If your antique is made from pine or a similar knotty softwood, apply an alkyd primer such as Kilz. If the finish looks splotchy or covers unevenly, apply a second coat. One way to avoid this is to spot-prime any knots an hour before applying the primer to the overall surface. Most alkyd primers carry a health advisory that recommends applying the paint in an open, well-ventilated area.
Antiques from the 18th, 19th and early 20th century often used shellac varnishes. As it happens, shellac is also an excellent primer that blends well with old finishes. Although you could use a clear or amber shellac, a white pigmented shellac primer covers any defects in the original stained surface and also lets you know where you've applied the primer. The shellac will help repair any small scratches and irregularities in the old varnish.
If your antique has a lacquer finish, a conventional primer might not bond effectively. A low-VOC water-based bonding primer will do a much better job of gripping onto the surface, and that will help the finish coat adhere properly for many years. A bonding primer eliminates the need for stripping or sanding the antique's surface, which might damage delicate older wood. Allow the bonding primer one to two hours to dry before applying any follow-up coatings.
Antique dealers use finish restoring treatments to reconstitute damaged varnish finishes. These products contain a weak solvent that softens the original finish and allows it to be buffed smooth again without the time, effort and expense of stripping and revarnishing. Although distressed finishes can provide an attractive decorative effect on antiques, for most projects a smooth finish will seem more appropriate, and using a finish restoring treatment before priming is an easy first step.