Old wooden deck railings. Need to be coated over, advice?

My deck floors and horizontal surfaces (rail caps) are new. Dried out now and ready for staining. My question is for my old railings / ballausters...they are coated in what seems to be a cheap stain that did not penetrate. I had Behr on another deck and it seems like that to me. I tried stripping it last year and got one post done after far too much hassle. Figure I’m better off covering it, as it’ll never match the new wood anyway. 

Will a solid stain adhere to this after sanding the worse areas and washing the whole deck and railing?  Do I need to prime first before solid stain?  Should I just paint it instead?  What product would be best?

i was leaking to towards flood but when I was at PPG they seemed concerned that it wouldn’t adhere. 

Sherwin Williams is attractive right now because it’s 40% off weekend but seems to have mixed reviews as far as their solid stains go.