Will it clean yes....it's soap by definition and soap cleans. Will it have much lather or other properties we look for in a bath soap, meh... not so much.
My cleaning soap is actually 100% coconut oil, lye and water and that's it. I also dropped the superfat to zero because I want it to clean and not have those leftover oils that the superfat offers. Especially true if it's used on clothing stains. Coconut oil is one of the cleansing oils which is why I chose it. I made 100% lard soap some time ago and I wasn't very happy with the results. Personally I don't get what all the fuss is about about soaps made with a high percent or 100% lard. Yes my 100% coconut oil soap is harsh on the skin but I use gloves when I use it. But it's good stuff......
IMHO if your going to make a bath soap you need to use castor oil and coconut oil. Plus other great oils to balance the whole thing out. IMHO also most soapers don't use enough castor oil. Castor oil is great because it adds lather but instead of being drying like coconut oil it's moisturizing. So it's all about balance in the whole recipe.
I recently made a soap with (experiment with a purpose as a recreations to a vintage product)
15% Coconut Oil
15% Castor Oil
and I'm not overly happy with it. Granted it's less than a week old, but the lather is disappointing, very disappointing. I did superfat it at 10% as well, so that does leave more oils leftover that can play havoc with the lather. But I also don't normally use that much tallow as one of the base oils.
Yes it's possible to make a cheap soap, but cheap and good I don't think are often said in the same sentence. IMHO Of course you could also give 100 soapers the same bar of soap to try and you will get quite a few opinions as it depends on their their personal opinion on what "good" is. Some are happy with plain jane while others won't be. I also think those that are new to soaping would think "anything" is wonderful because they haven't experimented to know the difference between what the different variations can offer in the finished product.
Me, I like the lather I get from coconut oil, palm kernel oil and/or castor oil. If you use too much coconut oil or palm kernel oil the soap will be drying to the skin even if the lather is lovely. So it's all about balance. But also about using other oils to make a great finished product.
If you wanted to keep it simple and cheap perhaps something like this.....
Olive Oil% 23%
Castor Oil 15%
Coconut Oil 22%
Bubbly Lather 29
Creamy Lather 36
You can buy some of those oils in smaller bulk or by the pound on some sites such as...http://www.soaperschoice.com/cgi-soaperschoice/Web_store/web_store.cgi?query_price_low_range=0&cart_id=http://www.wholesalesuppliesplus.com/Default.aspx
I do want to point out a recent blog post made by AM from BB about olive oils. Apparently not all are created equal and cheaper brands and smaller bottles are poorer quality. There are some pictures that speak a thousand words!!!! So I may also suggest buying your OO from one of the above (or other) reputable suppliers. http://www.soapqueen.com/bath-and-body-tutorials/tips-and-tricks/olive-oils-created-equally/
So if your going to take the time and spend money on ingredients, use quality ingredients so you don't have some ugly looking soap in a short time because of using cheap ingredients. You get what you pay for sometimes with "cheap".
While plain soap is fine and dandy you may prefer scented soaps. For more inexpensive scents you may want to look at http://www.naturesgardencandles.com/candlemaking-soap-supplies/category.cgi
although their shipping can seem high for smaller orders. But if you want some other inexpensive scents check out wholesale supplies plus (link above) some of their scents are cheaper while others are more expensive. Check out the reviews some do great in CP others don't and yes some discolor because of vanilla or other notes.
Above all get a good digital scale and weigh everything out in grams rather than ounces. There are 28 grams to the 1 ounce so you can see why it's more accurate. Use a lye calculator always to figure your recipe, and write out your recipe with a column for how much to add and how much you actually weighed out. Write that last part in by hand as you add it. That way you make sure you add everything and nothing is forgotten and you end up with lye heavy soap.