Clean and fillet fish (steps 1 through 3 of “You Found the Fish,” below). Put in a shallow 8- or 9-in. glass baking dish.
Combine 3 tbsp. vinegar, the lemon juice, 1 tsp. salt, and 1/4 cup water in a cup. Pour over fish. Chill, covered, 2 hours.
Combine remaining 1 1/2 tbsp. vinegar, 1/2 tsp. salt, the oil, and pickling spice in a large bowl. Set dressing aside.
Simmer potatoes in a small saucepan with water to cover until tender when pierced, 10 to 15 minutes. Drain, let cool briefly, then quarter and return to pan. Mix gently with half the dressing and let cool.
Add peppers to remaining dressing and let stand until ready to serve.
Drain fish and cut into 1 1/2-in. pieces. Mix gently with pepper mixture. Add salad mix and potatoes and toss to coat.
You Found the Fish–Now What? Some markets will clean them for you, but if not, you can do it yourself easily enough–it just takes a little practice.
SCALE AND CUT. Scrape off the scales gently with fingertips. Cut through both sides of belly 1/4 in. from edge, from collar to tail.
CLEAN. Pull out the guts; rinse the fish inside and out. Snip off fins.
FILLET (RAW). Score fish all the way around collar just to the bone. Slide your index finger into cut on one side of collar and your middle finger into the other side. Slide your fingers along spine to tail, pulling fillets free. Cut off tail and pull out any remaining bones.
FILLET (COOKED). Make 3 cuts through flesh to bones: along the length of the spine (to one side of it), at collar, and just above tail. Slide knife under fillet to free it from spine, and lift it off. Pull up tail and lift off spine and head to free bottom fillet. Pull out any remaining bones.
Note: Find these little fish at some grocery stores, fish markets (you might need to order them), and Asian markets. If you live near a coastal town, head to the docks-fresh anchovies and smelt are often sold as bait. Look for fish with bright eyes, shiny skin, and a mild aroma. They’re very perishable, so plan to cook them the same day.