+1 Seal MDF with primer. Zin Bin shellac primer works, and it good choice under spray lacquer.
+1 Polyester resin.
Many pro speaker builders will skip primer on MDF and use polyester resin used on fiberglass vehicle panels to stabilize and seal MDF. Then they use automotive painting methods for perfect paint job. PVA glue creep is common issue on MDF painted panels. Either use resin glue (urea is common), or cover the glue joints with 3-4oz fiberglass fabric and 2 coats of resin, then blend the edges with Bondo, sand/fill to get flat-ish surface.
Suggest two different paths as 'most likely to succeed':
1) Plain old 'instrument' or 'furniture' lacquer:
Easier to complete in home shop. Not most durable finish, and intolerant of cold glassware stored top. Can troll the guitar making forums for tons of different finishing schedules.
Seal MDF with shellac or WB primer, and sand perfectly smooth. Seal with rattle can automotive lacquer primer for even base color. Choice of sealer color depends on desired effect. Can use silver, with tinted clear coat to create candy effect. Can use white for bright red tinted lacquer. Latest trend is to use black sealer coat, followed by clear lacquer with colored pearl additive. Follow with 2 coats of clear on top. Hard part about lacquer is thickness limits. Thick lacquer does not move with wood, and can crack/craze. Using MDF helps, and allows a little more film build; but still requires spraying practice/experience, where you measure wet film build as you develop the finishing schedule to stay below maximum limits. The lacquer suppliers provide data sheets and application guides to help you figure it out.
2) Automotive finish: primer, base coat, clear coat.
Not to hard to accomplish at home. Though some states (Kalifornia+) have banned automotive paints in residential areas.
IMHO - Best protection is developed with 2-part urethane primer/sealer, and 2 part urethane clear. But even the worst auto enamel/urethane paint will be much more durable than regular nitro lacquer, and more tolerant of beginner spray mistakes. Automotive finish options are numerous, and local supply can dictate what folks think is 'best'.
Suggest looking into Omni or Nason urethane for base color coat. Can use enamel for color coat, but need to use enamel hardener making the color coat a 2K layer. The cost difference for easier to handle 1k urethane is higher, but overall costs are lower after adding in the enamel hardener. U-Pol makes an inexpensive 2K urethane primer/sealer that covers just about any base material and works under those base coats. They also sell a decent clear coat that uses the same catalyst, which can reduce cost on small jobs. If speakers were to be stored outside, U-Pol would be called a cheap 5 year paint job. But indoors it will last lifetime.

Automotive paint is not cheap; figure ~$45 qt kit of primer/sealer, $50 qt of base coat, $100 for 'gallon' kit of clear (no one sells quarts of clear). By time you buy reducer and/or retarder with right temperature for the job, looking at $250-$275 out the door where I shop. The same set of materials would paint entire front end on a small vehicle, and should be enough for 2 tower speakers (even if you goof a little).
Best Luck.