Congratulations on obtaining your permit and exercising your Second Amendment rights.
Your best bet is to find a local range with a large selection of rental guns. Try as many as you can -- different calibers, different brands, different sizes, etc. -- the more the better.
For more specific recommendations we will need to know more about how you intend to use your first gun.
Will it be used for home defense? Concealed carry? Just range and target shooting? Or some combination thereof?
A nice and well-made .22 LR semiautomatic, like a Ruger Mark III or a Browning Buck Mark, is an excellent first handgun for range use and learning the basics of shooting. The .22 LR round has very little recoil and is dirt cheap to shoot. However, it is not an effective round for self defense purposes.
A full-size 9mm semiautomatic, like a Glock 17 or a Sig Sauer P226, is an excellent first handgun for home defense. Loaded with proper ammunition (high-quality hollow points), it is an effective self-defense caliber. Recoil is significantly more than .22 LR, but less than larger calibers like .40 S&W or .45 ACP. It is also generally the cheapest effective self-defense ammunition.
A subcompact 9mm semiautomatic, like a Glock 26 or Kahr CW9, is an excellent first handgun for concealed carry. Felt recoil can be significantly higher in these small, lightweight guns -- shorter barrels, smaller grips, and less weight all contribute to an increased amount of felt recoil compared to full-size handguns.
All of the above recommendations for specific guns is not a full list of which guns are good choices for the various roles. They are simply representative examples of what is out there, and should be considered simply as a starting point and not specific recommendations. There are too many good handguns for an exhaustive list, and in your "hands-on" testing you may very well find a brand or model of gun not listed above that works much better for you. Remember that in the end, you will be the one purchasing the gun, and you will be the one shooting the gun. It is therefore of paramount importance that you find the best gun that fits your hand well, that you are able to shoot well with, and that meets your specific requirements.
Also, you mentioned that you want a semiautomatic pistol, but please don't discount revolvers. Be sure to try a few revolvers before making your final choice. You may find that a revolver might work better for you. Many people think of revolvers as more "primitive" handguns, but that is an incorrect assumption. The choice of a semiautomatic versus a revolver is oftentimes a heated debate, but in the end, each have their own benefits and disadvantages.