I am not sure how much you know about guns yet, but there are multiple things to consider when deciding on your first gun. You already mentioned that your primary purpose is home defense and something fun for the range. You also mentioned that you prefer semi-automatics to revolvers.
Caliber: The caliber of your gun should be one of the first things to consider since it will determine the cost and availability of ammo, the recoil, and to some degree the "stopping power". I am not going to start a caliber war so I'm going to leave stopping power alone, other than to say don't go below 9mm.
- 9mm: The 9mm is cheaper to feed at $.22 - $.25 per round and it is fairly easy to find these days. Recoil is lighter which makes it easier to shoot, but less "boom" may affect the "bad assery" of your gun. Smaller sized round usually means larger magazine capacity for the same sized gun.
- .40 S&W: Ammo is around $.32 - $.36 per round these days and is readily available. During the ammo shortage, it was one caliber that was still pretty easy to find. Recoil is a bit heavier than 9mm and a bit snappier. The round is slightly larger than the 9mm so you only lose a few rounds of magazine capacity compared to 9mm.
- .45 ACP: Ammo is a bit more expensive at $.36 - $.40 a round, but is fairly easy to find these days. Recoil is a bit heavier, but not as snappy. Most would say the .45 ACP is a pretty bad ass round. The .45 is larger in diameter and length which means lower magazine capacity and a slightly larger grip than 9mm or .40 S&W.
Trigger Type: This is getting a bit harder to classify these days, but I will try to simplify it.
- Single Action Only: The means that the only thing the trigger does is drop the hammer. The gun must be cocked in order for it to fire. Since we are talking about semi-automatics, it will obviously cock itself after each round. Pretty much all SAO guns have a manual safety. The trigger is usually shorter and lighter than any of the other trigger types, making them nice for the range, but possibly less-suitable for beginners. The most common SAO guns are 1911s.
- Double Action Only: The trigger brings the hammer back and drops it with each trigger pull. This is a long trigger pull and usually a bit heavier. This mimics a revolver's trigger pull. While it is "safer", it is less fun at the range. Most DAO guns do not have manual safeties. This is usually a trigger "option" on DA/SA guns.
- Double Action/Single Action: This type of gun is usually carried with the hammer down unless there is a manual safety. The first shot usually fired double action which is a longer heavier trigger pull. All subsequent shots are single action, which is a shorter and lighter trigger pull. This is a very common and popular trigger type and is seen on Sig Sauer's P22X series of guns, Beretta's 92/96 guns, and many others. Many DA/SA guns have safeties that double as decockers or they may have decockers only.
- Striker Fired: While this isn't a trigger type per se, most striker fired guns operate in a fairly similar fashion. Almost all striker fired guns have the striker in a partially cocked position. The trigger pull brings back the striker the the rest of the way before firing. The trigger pull is longer than for SAO guns, but most are fairly light. For follow-up shots, most striker fired guns have a short reset which does not require the trigger to go all the way forward before being fired again. Glock was one of this first (with the exception of H&K) to make striker fired pistols. Many striker fired guns do not have manual safeties. Springfield Armory's XD line of pistols add a grrip safety similar to those found on 1911s. Walther's PPQ is another very popular gun that is striker fired.
Metal vs. Polymer: This is mainly a weight and appearance thing. Some people do not feel comfortable carrying a "plastic" gun even though Glock has proven how tough polymer guns can be with their torture tests.
With all that said, here are some recommendations in no particular order:
Sig P229
CZ-P07
CZ-75 SP-01
Walther PPQ
Glock 19
Beretta 92 (M9)
Springfield Armory 1911