Basic Information
There are two basic types of MAP base soap:  clear and white, or opaque.  From there, it's a matter of formulations.

Clear Glycerin (usually a non-suspension base)
Clear glycerin is an excellent choice when embedding things in soap and when you want the clearest possible finished product.  Though heavier additives will sink and lighter additives will float, soap glitter works exceptionally well in this base, as do jojoba beads.  Use of clear liquid colorants is recommended in order to maintain clarity.  Some fragrance oils, however, will cloud clear glycerin.

Olive Oil Glycerin (generally a suspension base)
Still considered a clear base, olive oil glycerin is a lot cloudier than the clear glycerin, and has a slightly greenish hue that may affect colorants.  In addition, it carries a little bit of an olive oil scent which could impact your fragrance.  It is often sold as a suspension base formula (read the label to verify this) which means additives will remain better distributed throughout the soap instead of settling to the bottom or floating to the top.  Obviously, olive oil glycerin contains olive oil and, therefore, offers all of the skin-nourishing qualities of olive oil.  Olive oil is said to be soothing to burned or inflamed skin and moisturizing or healing to dry skin.

White Glycerin (typically a non-suspension base)
An excellent basic soap choice, white glycerin colors well for solid-colored soaps and crayons make an excellent alternative to liquid colorant as, with this soap base, opacity is a given.  However, as a non-suspension base, you may find that additives, such as herbs, either float to the top of the mold (which will be the back of the finished soap) or settle to the bottom of the mold (the top of the finished soap).  Additionally, non-suspension base soaps do not perform as well with techniques such as marbling.  As the colorant is not completely blended into the melted base, the color or colors may also either float or settle.

Goat's Milk Glycerin (most often a suspension base)
Another opaque or white base, the natural emollients found in goat's milk are reported to be effective in soothing some skin conditions such as dry skin, psoriasis or eczema.  The suspension base quality, particularly when paired with the skin-smoothing properties of goat's milk, make this an excellent choice for soaps that include herbal additives.  This particular formulation also seems to be more readily available at craft stores than some of the other opaque suspension formula bases.

Shea Butter Glycerin (normally a suspension base)
An opaque or white base, shea butter glycerin is also most often sold as a suspension base.  Historically prized for its anti-aging properties, shea butter has been sold for decades to diminish stretch marks on the tummies of expectant mothers.  It is also often used to soothe burns and rashes and is found in many lotions and creams used to lighten or reduce the appearance of scars.

Avocado Cucumber Glycerin (another suspension base)
An opaque soap base, this particular glycerin in not quite white, picking up a slightly, lightly, greenish hue because of the avocado and cucumber formulation.  Typically sold as a suspension base glycerin, it embodies the cooling properties of cucumber as well as the many moisturizing qualities of avocado oil.  Widely used in skin repair and rejuvenation lotions and creams, avocado oil is readily absorbed by the skin, making it ideal for sun-damaged and severly dry skin.

About Formulations
None of the glycerin soap bases carry the full-strength properties of their formulation additives (olive oil, goat's milk, etc.).  However, the soap bases do offer a diluted version of the properties inherent in the additive.  This is important to know because you have the option of mixing your own soap bases.  You can add anti-itch lotions, astrigent creams, antibacterial salves or pain-relief ointments to any opaque soap base to add or enhance those qualities in the soap.  Obviously, you need to be rather conservative in the amount added or you may inhibit the soap base's ability to harden or lather.  For this reason, I recommend that you include these additives in soap bars of 4 to 5 ounces (or larger) and that you add no more than 1/2 Tablespoon to any given bar.  Additionally, do not add the lotion, cream, etc. until after the soap base has been melted as it may be unsafe to microwave it and doing so may also affect the effectiveness of the additive.  You will also want to stir-cool the melted soap base prior to adding any of these enhancers as the higher temperatures may break them down beyond their usual level of effectiveness.

There are, with various online vendors, other MAP soap bases available.  Many of these special formulations carry the name of the online company, suggesting that the vendor may be making and marketing the base.  These include aloe vera; honey; hemp; cocoa butter; green tea and hibiscus; rosehip and jojoba; oatmeal, and seaweed.  As the market for homemade soaps expands so, too, may the MAP soap bases which are locally available

When adding any medicinal or cosmetic cream, ointment, lotion, etc. to your soap base, it is critical that you thoroughly read the manufacturer's label information to determine whether or not that material may be volatile when exposed to heat.  Any warnings which pertain, for example, to possible allergic reactions, must be considered and that information must also be included on the label you make for your soap.

Some possible soap additives inlcude:  cocoa butter, calamine lotion, petroleum jelly, mentholated skin cream, vitamin E and antibacterial ointment.