S-04 and S-05 are not "generic" yeasts, whatever that means. 04 is an english ale strain, while 05 is the same "chico" strain that is in liquid form by both wyyeast and whitelabs. 05- is a clean, neutral ale yeast used for many american ales, whether they are IPAs or Stouts.
I think if you want to "learn" about yeasts you have to learn that there are very few "generic" yeasts...again I am not sure what that means. Every yeast whether liquid or dry has specific uses. And Liquid and Dry both have their place.
I have found that a lot of new brewers especially, THINK they HAVE to use liquid yeast, but in reality most ales can be made with Notty, Windsor, Us-05, Us-04 and many lagers with basic Saflager.....7-8 bucks a pop for liquid as opposed to $1.50-2.50 for dry, with more cell count, is imho just a waste of money for the majority of a brewer's recipe bank...most commercial ales us a limited range of strains, and those liquid strains are really the same strains that the afore mentioned dry strains cover, for example Us-05 is the famed "Chico strain", so if you are paying 7-8 bucks for Wyeast 1056 American/Chico Ale Yeast, and you STILL have to make a starter to have enough viable cells, then you are ripping yourself off, in terms of time and money....
I use dry yeast for 99% of my beers, for basic ales I use safale 05, for more british styles I us safale 04 and for basic lagers I use saflager..
The only time I use liquid yeast is if I am making a beer where the yeast drives the style, where certain flavor characteristics are derived from the yeast, such as phenols. Like Belgian beers, where you get spicy/peppery flavors from the yeast and higher temp fermentation. Or let's say a wheat beer (needing a lowly flocculant yest) or a Kholsch, where the style of the beer uses a specific yeast strain that is un available in dry form.
But if you are looking for a "clean" yeast profile, meaning about 90% of american ales, the 05, or nottingham is the way to go. Need "Bready" or yeasty for English ales, then 04 or windsor. Want a clean, low profile lager yeast- saflager usually does the trick.
Here's some reading for you.
One way to explore yeast is to brew what we call "smashes" Single malt and single hop beers. That are basically that, one grain (extract or grain) and a single hop...in your case you would brew the same basic recipe but change the yeast strain. One way would be to brew a 5 gallon recipe, split it intom 2, 3 gallon water jugs, carboys, better bottles, or mr beer kegs, and pitch a different yeast in each.
But I think the first thing to learn about yeast, is to drop any pre-conceived notions that you might have that dry is somehow inferior to liquid yeast. Even Palmer, in How to Brew, doesn't bash dry yeasts...
Yeast come in two main product forms, dry and liquid. (There is also another form, available as pure cultures on petri dishes or slants, but it is generally used as one would use liquid yeast.) Dry yeast are select, hardy strains that have been dehydrated for storability. There are a lot of yeast cells in a typical 7 gram packet. For best results, it needs to be re-hydrated before it is pitched. For the first-time brewer, a dry ale yeast is highly recommended.
Dry yeast is convenient for the beginning brewer because the packets provide a lot of viable yeast cells, they can be stored for extended periods of time and they can be prepared quickly on brewing day. It is common to use one or two packets (7 - 14 grams) of dried yeast for a typical five gallon batch. This amount of yeast, when properly re-hydrated, provides enough active yeast cells to ensure a strong fermentation. Dry yeast can be stored for extended periods (preferably in the refrigerator) but the packets do degrade with time. This is one of the pitfalls with brewing from the no-name yeast packets taped to the top of a can of malt extract. They are probably more than a year old and may not be very viable. It is better to buy another packet or three of a reputable brewer's yeast that has been kept in the refrigerator at the brewshop. Some leading and reliable brands of dry yeast are DCL Yeast, Yeast Labs (marketed by G.W. Kent, produced by Lallemand of Canada), Cooper's, DanStar (produced by Lallemand), Munton & Fison and Edme.
Dry yeasts are good but the rigor of the dehydration process limits the number of different ale strains that are available and in the case of dry lager yeast, eliminates them almost entirely. A few dry lager yeasts do exist, but popular opinion is that they behave more like ale yeasts than lager. DCL Yeast markets two strains of dry lager yeast, Saflager S-189 and S-23, though only S-23 is currently available in a homebrewing size. The recommended fermentation temperature is 48-59°F. I would advise you to use two packets per 5 gallon batch to be assured of a good pitching rate.
The only thing missing with dry yeast is real individuality, which is where liquid yeasts come in. Many more different strains of yeast are available in liquid form than in dry.
Liquid yeast used to come in 50 ml foil pouches, and did not contain as many yeast cells as in the dry packets. The yeast in these packages needed to be grown in a starter wort to bring the cell counts up to a more useful level. In the past few years, larger 175 ml pouches (Wyeast Labs) and ready-to-pitch tubes (White Labs) have become the most popular forms of liquid yeast packaging and contain enough viable cells to ferment a five gallon batch.