From another post, I believe you are in the Jackson area? Cliff is a great resource; definitely send him a PM.
In the central Mississippi area, you'll have lots of choices for handgun competition. Although there will be experienced shooters in most any sport, most groups will be very willing to help you get back into things. There is no "defense" in shooting sports, so really your biggest competition will always be yourself. With your background, I'm sure it won't take long for you to get the hang of whatever sport you try. In the interest of full disclosure, I am the Mississippi Section Coordinator for the United States Practical Shooting Association (USPSA) and have been shooting matches for about 10 years. I've also shot steel challenge matches and a couple Cowboy Action ones, too. I say this because I don't want you to think I am trying to sway you toward or away from any particular competition. I have more knowledge about some than others, but by all means try as many as you can or want to. They all have their merits and fans, and only you know what you enjoy.
On the 1st Sunday of every month, there is a USPSA match in Byram. USPSA matches attempt to mix of speed, power, and accuracy, and are a lot of fun. I believe I read that you had a Sigma, which would work in Production Division, and a Ruger 45 which would work in Limited 10 Division. If you have any questions about the sport or the divisions, feel free to contact either me or Cliff. There are a good many other USPSA shooters here as well, and some good info in the USPSA section. One thing USPSA does is allow you to get "classified" where you can compete against people of your own skill level, or "class" within a particular division. This lets a new shooter with basic equipment compete against others similarly situated instead of having to worry about experienced shooters with "race guns". The Byram club's website is www.teammagnolia.com
. As a side note, their match this weekend is a special classifier match. If you think you might be interested in USPSA, this would be a GREAT match to make. You'd need less equipment than a regular match and can go ahead and get an initial classification if you join the national organization either before or shortly after the match. The match this weekend won't be quite as much fun though as a regular montly (well in my opinion anyway), but it will still be fun.
On the 2nd weekend of the month at the same place, you can shoot Renegade Steel matches, which are speed steel matches similar to the Steel Challenge. Either your Sigma or Ruger would work. Cliff helps run the program and would be a good person to talk to. Steel is a simpler match than USPSA, but there are no classes and fewer divisions, so you will be lumped in with everyone a bit more.
On the 3rd weekend of the month, also at the same place, you can shoot International Confederation of Revolver Enthusiasts (ICORE) matches OR Silhouette. ICORE will let a new shooter use a semi-automatic for their first match, but as the title indicates, is a revolver only competition and is similar, in some ways, to USPSA. Silhouette is longer range shooting at steel animal silhouettes, and they shoot both .22 and large bore handgun silhouette in Byram.
A full list of the match schedule in Byram can be found here:
Of course if you want to travel a bit there are even more options, including Cowboy Action Shooting just down the road in Mendenhall and NRA Action Pistol further south. Like Cliff said, just let us know what gun you want to shoot and ask as many questions as you like, many here would be glad to help.