Now here is a subject that was easier to answer a couple years ago than it is today and yes there are many variables here as well. We will try to keep the answer informative and concise.
To start with there are three basic physical battery types used in conversions:
Prismatic cells (built like a brick with ridged exterior dimensions);
Pouch cells (soft and flexible like the name implies); and,
Tesla popular cylindrical cell, similar to an AA battery, only larger.
All three physical types are available with several popular chemistries. Most, but not all, Prismatic cells are described as a Lithium Iron Phosphate chemistry. They are considered the safest chemistry. Typically, Prismatic cells have a 3.2v nominal voltage and are what we call "a little sleepy", meaning they don't accept or release electrons quickly. This is an OK battery for most DIY builds and less than high performance vehicles.
Other popular chemistries are Lithium Polymer, Lithium Nickle Manganese Cobalt Oxide, Sodium, Nickle Silicon Aluminum and Sulfur. Some of these performance cells offer 3.7v or slightly higher nominal voltage. All of these have a lithium solution and the other words found in the cells name generally describe the material or coatings used in construction of the cell and primarily the anode and cathode (positive and negative polls) within the cell.
Billions of dollars have been spent on battery improvements over just the last few years and even more will be spent over the next few years to maximize the energy density, longevity and charge cycle capability. The next great gain in battery cell technology will be the solid-state battery offering many advantages over today's liquid lithium solution cells.
Which is best for you is a complex subject. Many of the converters today are using used Tesla modules from salvaged vehicles. A typical Tesla module holds 444 individual cylindrical cells and can be used in both series and parallel configurations or combinations thereof to create the max voltage and amperage desired. Tesla uses 6000 to 7000 cells or around 16 of these modules in a single car. Last I looked the aftermarket was asking between $1200 and $1400 per module. Because these modules are becoming increasingly popular the prices are continually climbing.
There are of course many other options available. Most lithium-based batteries are made in either China, Japan or Korea and most have distributors in the US and Europe. If you are doing your own conversion and building your own packs then hit the Internet hard, see what others are currently doing and find your best deal. Ideally though, you will want to deal with a company who has experience designing and building battery packs. Safety and battery life come through proper battery management, so unless you have done this successfully, lean on others with a good reputation.