Well, starting with the catcher position is not only natural, but also the easiest position for me to select. Two catchers from 1985 on were easily head and shoulders above the rest: Mike Piazza and Ivan Rodriguez.
Piazza is easily the greatest hitting catcher of all time. If injuries wouldn't have taken their toll late in his career, he had a great shot at 500 home runs, instead ending with only 427. A sure fire Hall of Famer, Piazza was the 1993 NL Rookie of the Year. He was a 12 time All Star, grabbing the '96 AS Game MVP, and finished in the top five for MVP voting four times. Though pretty terrible on defense, his ability to get on base at a .377 clip and have a career OPS over .900 made him one of the best offensive players of the last 25 seasons.
Ivan "Pudge" Rodriguez may well be the greatest defensive catcher of all time. He has a career caught stealing percentage of FORTY-SIX PERCENT. That means nearly half of all would be base stealers get are throw out by Pudge. Not to mention he has had eight seaons where he has thrown out over half of would be base stealers. Add to that his career .299 batting average, 14 All Star games, 1999 MVP, 2003 NLCS MVP, durability, longevity and outside reach at 3,000 hits (he is currently sitting at 2,711) and you have a surefire Hall of Famer.
So, the All Quarter Century team starts out strong, with two extremely talented offensive catchers and one of them a defensive wizard behind the plate. Next up: Corner Infielders.