What kind of seaweed do I need for Japanese-style seaweed salad?
Because we don't do recipe requests around these parts, I'm going to treat this as an ingredient question.

Japanese markets (and some online merchants, including Amazon) often sell dried versions of the seaweed mix that many restaurants use. It'll be sold as kaiso salad or seaweed salad. Some versions are better than others; some contain a ton of dyes that make the salad look unnaturally neon to my eyes, although the taste and texture is similar. Such blends typically contain wakame and other seaweeds, including agar agar noodles, for example.

If not included in the package, you can make a simple dressing based on toasted sesame oil and Japanese vinegar, in roughly a 1:3 ratio, or use sesame oil and lemon juice (maybe 1:1-1:2 ratio since it's more acidic). You may want to include soy sauce or salt. This is loosely in the category of sunomono, so it doesn't typically contain emulsifiers like mustard, but if you find it hard to blend you can use a touch of mustard or something like lecithin or a stabilizer like xanthan gum.