This will be my second year of having my own garden, so I offer only enthusiasm and not much experience. I love starting things from seed, indoors and out. The choice of varieties is so much greater with seed than with plants. The up-front cost of seed is lower (though I guess you'd have to factor in success rates, and the extra effort). And I just love seeing the sprouts come up. I get more out of that than from the harvest, I think.
I had good luck starting tomatos and peppers indoors last March. I did buy a 2-tube flourescent work lamp to put over them. ($20 or so at Home Depot). I had less luck with lettuce started indoors, and peas -- weak and lanky. They both did much better planted directly outdoors.
My mom's the expert gardener, and she always planted peas, beans, corn, carrots, radishes, melons, lima beans, that's all I can remember now, from seed direct in the garden, and bought tomato plants. She didn't grow peppers, or start anything inside.
Best of luck.