For target shooting, you will want the target version of whatever gun make you decide on. The reason is simple - weight. Target versions tend to be, on average, a pound heavier than the corresponding field version. Target guns get shot a lot and carried a little, so weight becomes your friend in the recoil department.
Used - Browning Gti, 325, 425, 525 might be in the ballpark figure, as well as some of the Beretta 68X versions - both makers are still in business; every gunsmith who actually is one can fix them easily, parts are available; and their longevity has been proven. I do not think you will find a target version new in your price range.
SKB -I'll categorize SKB as just slightly lower than Beretta and Browning, but not by enough to matter to most. However, SKB in Japan stopped production. The US importer, GU from Omaha, has guns and parts, they say, to last for several decades, and they say they are trying to find someone to resume production. SKB made Weatherby at one point and several others. If it looks like a Merkel but was made in Japan, it most likely was made by SKB.
It really comes down to your volume of shooting. My Gti, now 17 years old, has about 200,000 rounds through it. I have had the main spring, firing pins and firing pin springs replaced once - at about 90,000. As mentioned, one advantage of a mainstream gun is that my smith can not only fix this gun, he keeps all the parts in stock because they are popular and he sees a lot of them over the course of a year - (He lives at a retirement gun club in Fl)
As for the type of gun - IMO, it is easier to shoot trap with a skeet version stock, than the other way around. Trap versions are typically set up to shoot a high POI/POA - around 70/30, whereas skeet guns shoot typically 50/50 or at most, 60/40. Since you have targets that are not all rising as in trap, the skeet version will be better at not having you missing over the top on birds that might be dropping.
Besides, eventually, you'll want to test the waters at the 5-stand, sporting clays, and maybe even the FITASC fields.
Good luck!