For a beginner in either sport find a nice used Remington 1100 or 1187, For about $600 you can buy the gun and have an adjustable pad installed if needed. This will help in making it fit, some trap models have a MC stocks also.
When you decide which sport you'll enjoy most (trap for me) then find a nice trap gun and have it fitted to you. A nice trap gun can be a single barrel, O/U , pump or Semi-auto.
They are all made in a trap configuration. Fit is more important than looks or action type. If you are going to shoot doubles in trap then only a semi-auto or O/U will work, if you chose only 16 yd and handicap birds, a nice single barrel BT99 or Remington 90T are great entry level guns.
I've been shooting trap for 30 years but only registered trap for the past 4. Typical for trap shooters in the past 4 years I've bought , shot and sold a Browning Citori Trap, Rem. 1187 trap, Remington 3200 Special Trap, Remington 90T, Browning Ultra XT, Browning Citori Trap Plus, Browning BT99, Kreigoff KS-5, and have finally settled on a Kolar combo. If you really get into the sport you'll go through your fair share of guns too.
Good luck, have fun, enjoy shooting.