Knots bleed because the resin in them is still active, and ordinary water-based primers, undercoats and even most oil primers can't stop it. The resin migrates up through your paint film and you get that horrible amber halo, usually weeks after you thought the job was sorted.
The fix is shellac. Reach for Zinsser BIN — it's the gold standard for knotting. Shellac is the one thing that genuinely blocks the resin, and BIN dries in 45 minutes so you're not hanging about. Dab it neat onto every knot with a small brush, then once it's touch-dry give the whole piece of timber a full coat as your primer. On really live knots (fresh pine, anything weeping sticky resin), hit them twice. Old-school traditional knotting compound exists, but it's fiddly and BIN does a better, more durable job.
A word on the order of work: sand the bare timber, dust off, then shellac the knots, then prime the whole surface, then undercoat and topcoat. Don't skip the full prime coat just because you've spot-treated the knots — you want a uniform sealed surface for your finish to grip.
For the topcoat itself, once everything's properly sealed you can use any decent trim paint. Little Greene Intelligent Eggshell or Dulux trim are both solid on woodwork, and if you want a tough, hard-wearing finish on skirtings and doors they'll hold up nicely. Whites that sit well against most walls include Farrow & Ball Wevet or Pointing for a soft warm trim, or Strong White if you want something cleaner.
One last thing — if your timber's already painted and a knot has come through, you can't just slap more topcoat over it. Sand back to bare wood at the knot, shellac it, re-prime, then repaint. Painting over the bleed without sealing will only buy you a few weeks before it ghosts through again. Do it properly once and you'll never see that knot again.