The appropriate tool is the one that works. Vic Reinders won the Grand many, many years with a Remington Model 31 pump, as did Rudy Etchen and Daro Handy with Remingtin 870's. I've shot many a 25 with a Model 870 myself.
Pumps were more popular from the 40's to the 80's, first the Win. Model 12, Rem. Model 31, and the Rem. 870. Most people shooting trap with a pump today do so because it's their only shotgun, or for nostalgia. You do have to get very fast with a pump to score good on doubles. I was Ok with my 870, but I'd prefer my 1100 Competition for doubles these days. (My singles and handicap gun is a Ljutic single barrel trap gun.)
Your money would be far better spent on a good pump than that Legacy. Your 500 will work, like George P says,
if it fits you. The fixed Modified barrel will be fine for 16 yard singles. 12 ga. is the only gauge to shoot for Trap, unless you are shooting a sub-gauge event.
If you have a bead, that is enough. You don't
aim a shotgun, like you do a rifle. I do recommend on investing in one of these;
https://www.midwayusa.com/product/1018129779
and experimenting with it at the patterning board to find a good fit that gives you a Point Of Impact higher than the 50/50 POI your 500 probably gives now.
At the point you are now, just get out and shoot; watch the best shooters at your club, and approach them for advice. They will probably advise you to get an O/U or SBT (Single Barrel Trap gun; BT-99, etc.) , but if you explain you're just starting out, they might let you try their guns. If they do, offer them a box of shell and a cold beverage of their choice for their generosity. You may find a gun that you just can't miss with; that's how I fell in love with Ljutic MonoGuns many years ago.
Oh, and watch this:
It's old but it's full of good advice. Just like the info in the pamphlet that George P. linked, I have the high schoolers I coach watch that video. You'll notice them shooting Rem. 8780's and 1100's in it. Those guns dominated the Trap fields in the 60's and 70's.