??
Might want to have another look at that stress figure. I come up with way higher. Too much deflection for a 14 foot span also.
If it's lagged to a couple of wooden posts. All that twang (technical term for deflection) will also pull at the posts. Less twang means less pull and a more vertical load at posts. You want to keep the deflection down to no more than .01 per foot. Less if you like big safety factor like me. Our overhead cranes at the shop have a 3x's plus factor of safety in them throughout. (but don't tell anyone here cause they might get the idea to put up heftier hoists and defeat my design intention...)
If the load of 1,500 is it... and hopefully with some bounce or safety factor included... I wouldn't go with anything less than a beam with a moment of 35 or more. That'd put you at a W6 x 20 (I=41.4) or a S7 x 15.3 (I=36.7). Butt... for another 14 lbs. of material over the W6 beam you could go W8 x 21 and get a nice hefty 75.3 moment and have that warm and fuzzy feeling of knowing the beam will handle double your estimated load. Or if headroom isn't a huge concern then go W10 x 17 and save weight / dollars and get a nice 81.9 moment.
I haven't purchased any structural steel in a good while but I can't imagine it'd be over a buck a pound for wide flange beams? (about 20 years ago I recall about 35 cents / lb.?) Regardless of per pound cost... adding a few pounds of beam for a nice gain in moment and further reducing the deflection is a win since only adding the cost of an additional few pounds of material.