When contemplating beginning your new endeavor of riding sidesaddle, there are a few basic steps to start with.
First, consideration must be given to the style and purpose for which you will be riding. Generally speaking, you will see western stock, English hunt, English park, and older "period" saddles which predate some of the "modern" designs of the western and English styles.
If you prefer western style, you will see a variety of sidesaddles built in the same style as a western astride stock saddle potentially from a broad span of time. The western style, in one form or another, has been in production from the late 1800's to this year. Some reflect more of a working saddle style with saddle strings, some are more highly decorated with intricately carved designs and silver conchos instead of saddle strings. The seats may have smooth or stamped leather, or a quilted suede seat. The rigging will also be similar to a western stock saddle with cinches and latigos.
If you prefer to ride in the English style, but have no intentions of ever purposely leaping over a fence or a downed tree, you likely do not need a hunt saddle reinforced for jumping. English park, or saddle seat, saddles were designed for light use such as a social ride through the park. However, if you are of the adventurous set, an English hunt saddle would be most appropriate since the tree itself is reinforced to withstand the impact of the hunt and leaping over obstacles such as fences, hedges, downed trees, sheep, goats, small children, etc.
If you are a historical re-enactor whose persona being portrayed is from 1840, that would predate some of the features of the modern English and western sidesaddles. Although some of these saddles were quite beautiful, with tapestry seats, trapunto quilting and sometimes even actual embroidery, most have not survived the turning of two centuries intact. If they have survived in good condition, the historical value may exceed the functional value and they really should be in a museum or kept for display as they are rare examples of the craftsmanship and design aesthetic of the era. If you happen to be a short petite woman riding a slender, high withered horse, you may be at an advantage if you choose to ride it. Some of these saddles have been restored, but most are not really compatible with the size and shape of modern horses or riders. You would not only find that these saddles are more of a challenge to find, but to fit and to ride as well.
In the same way that shoes of different brands fit differently, sidesaddles of different brands may fit differently. Once you have measured yourself (detailed here), and know what size saddle to look for, your quest begins. It is not unusual for riders to start with one saddle that is reasonably workable and then trade up when they find one that they find a better, more comfortable fit. In any case, it is always good to educate yourself and ask any questions (take pictures of anything you have doubt about) and any of the more experienced sidesaddle riders will be happy to share their knowledge and experience.