Some things to consider when choosing a spinning wheel?
What do you want to be able to spin?
All the wheels offered at Elizabeth's Fiber to Yarn will spin about any fiber you can come up with. Prepared fibers such as combed top or roving is a good place to start. The most common and readily available fibers are: Wool Fiber (shorn from sheep), from the finest Merino to Medium Fine Colonial, Corriedale wools and coarser varieties. Mohair (hair shorn from the Angora goat). Angora (wool shorn from the Angora rabbit). Alpaca (wool shorn from the Alpaca), Silk, cellulose fibers such as Tencel, Viscose and many more. If you primarily plan to be spinning fine yarns, then select a wheel with high ratios.

Drive ratio? Is the difference in size between the circumference of the drive wheel and the circumference of the flyer or bobbin whorl. This determines the amount of twist in a fixed amount of yarn. With each treadle push, the drive wheel revolves once. The flyer will revolve a different number of times, depending on the difference in its circumference. The smaller the circumference on the whorl the faster the the flyer will spin. If the flyer revolves 10 times to one drive wheel revolution (10:1) then 10 twists are put into a given amount of yarn for that one treadle push. A wheel that offers several drive ratios is a plus.

When I started spinning I wanted Angora yarn. That was a good goal, but soon found that some fibers are more difficult to spin than others. To help you succeed when you start out spinning chose a medium grade, long staple wool fiber, such as Corriedale, Blue Face Leicester or Romney.   Once you master these easy to spin fibers you will have an easier and more pleasant time when you progress to the finer merinos, alpaca, angora, silk and/or mohair's.

Castle or Upright Spinning Wheels   Does the wheel need to be portable? Do you plan to take your wheel with you while vacationing or traveling? Do you plan to attend spinning conferences and classes? Unless you have a large vehicle and strong muscles you will probably find the castle style of wheel more user friendly. Most spinners that really "get into" spinning will have a castle type of wheel as their second wheel for the ease of transport. The downside with most castle wheel is the wheel ratio will be less than a Saxony.    If your rig is large enough best to lay your Saxony down padded with heavy blanket and pillows. The castle style wheels fit on the seat of most autos belted in.
Is floor space a issue? Will you have to put your wheel away when not spinning?  The castle style wheel footprint is less than a Saxony therefore easier to store.
Is your height under 5 feet? You might find the orifice height of the castle wheel less comfortable than that on a Saxony. This isn't a real issue unless you are more comfortable having your hands situated right at the orifice. Once you become accustomed to spinning you will realize holding your hands lower, closer to you will be less tiring and more comfortable.
Back issues? If you have a back that tends to be sore. Then consider the castle wheel. This upright wheel is spun with the wheel in front of you. Making you sit straight and forward. Plus the orifice height is generally higher than a saxony style.
Want to spin large amounts of yarn or if you have trouble treadling, the electronic is your best choice. Excellent for plying, Fast, keeps consistent, huge bobbin will hold two regular bobbins worth of singles. Wonderful for spinning worsted weight soft twist singles. Quiet motor, direct drive flyer. Variable speed 0-1500 rpm. Hand control for on/off, reverse and speed.
Spin Thick   If your interest lies towards spinning thick rug yarns or Art Yarns then consider the Ashford country spinner.   There really is no other wheel to compare. It has a weighted wheel to aid in treadling. A super big bobbin (holds 2 lb.) and a orifice (the opening where the yarn must travel) that is almost an inch in diameter.    If your plans are to only occasionally spin bulky or Art yarns, then consider adding bulky flyers to your standard wheel.  

Saxony Style Spinning Wheels
These are the wheels that most think of when they think of spinning wheels. Saxony spinning wheels have been in use for hundreds of years. It is the most common and to many the most decorative. The wheel ratios generally will be higher than the castle style wheels. Bigger wheel- less treadling. So if you already like the looks of a Saxony, have the space in your home, and wish to spin yarns from lace weight to a heavy worsted yarn, then this style is for you.

Double Treadle or Single Treadle? If you plan to spin for long periods of time, most find the double treadle less fatiguing. With a double treadle you should be able to spin with just one treadle too and keep going if you need to stretch your leg or if for some reason fate breaks your leg.
Some wheels that have a double treadle option really don't help much in my opinion. Example the double treadle on the Ashford Joy is a bit overkill.   The Joy wheel is so small and lightweight having a double treadle is not really necessary. Another wheel I find the double treadle really not necessary is the Schacht 30" Saxony wheel. The wheel is quite large offering fast ratios, you actually are treadling about half as much anyway. I had to relearn my normal treadling and SLOW way down.

Double Drive or Single Drive? Using the double drive mode of spinning the drive belt goes around the wheel, the bobbin whorl and the flyer whorl. Double drive operation is one long band. It gives equal tension on the flyer whorl and the bobbin whorl. Making tension adjustments easy.
Using the single drive mode (AKA Scotch Tension) the drive band goes around the wheel and flyer whorl. A separate band, usually with a small spring, is applied to the bobbin whorl.
All the double drive wheels include the option of a single drive. The single drive option makes spinning lofty woolen type of yarn easier. Spinning in double drive mode aids in spinning yarns in a semi woolen, semi worsted or worsted spun yarns. Personally I think the double drive wheels that include the single drive option is the best of both worlds.

Does the wheel offer upgrades that I can add later?  Schacht Matchless, has several whorls that you can add later. Faster whorls when you progress to spinning lace weight yarns and slower whorls when you wish to spin thick singles or lumpy bumpy novelty yarns.
Ashford double drive offers a high speed whorl that will help you spin fine singles, that when plied together will result in a yarn similar to a fingering or sock weight yarn. Ashford single drive wheels offer lace bobbins if you wish to spin really fine yarns.

Most standard wheels have the option to add the bulky flyer.    These options not only are great to spin those thick yarns, but also be able to plylarger skeins.   Two standard bobbins just about fit on one of their bulky bobbins when plied.

Once you decide the style you want, either Castle or Saxony there are several options. The price may be a consideration for you. All are good spinners. Expect to pay more for features, such as wood, finishing, larger wheels and details on the craftsmanship.
Ashford wheels, made in New Zealand.  Most are available finished or unfinished completely un-assembled, shipped as a kit.
The Schacht wheels are made in the USA, comes finished and assembled.

Charka is a small spinning device with extreme high ratios designed for spinning cottons. Cotton fibers for charka spinning are available either in sliver or punis. I will confess, spinning cotton is not something that I have done.  If cotton is what you want to spin then the Charka is the wheel for you.

Elizabeth's recommendations:
If you know handspinning is your new passion or if you are looking to add or upgrade your current wheel, Then my best recommendation is the Schacht Matchless. If I could only have one wheel this would be it. This wheel is my workhorse. I can spin on it all day. With the optional whorls I can spin just about anything I can imagine. The workmanship and engineering of the Schacht wheel is unsurpassed over any other wheel that is readily available to the spinner. I also like the Schacht Saxony. It is so beautiful. I won't be taking this wheel to the fair or barn for spinning demos. It is my trophy wheel for my living room and when I want to spin fine yarns this is my wheel of choice.
If you are just starting out on your spinning adventure and not sure spinning is going to be your passion or if price is a consideration any of the lower priced wheels will do you well.    Take good care of your wheel and they will not loose their value.    You can always upgrade later, have a second wheel or share with a friend.