My experiences:
1) I got a promotional pen from someone, I used it few times, most of time it sits in my drawer. I did look at the website letters printed on it, but did not put in my computer to check out the website, I do not see big advertising function for a small pen, as no much room to tell other people what the company is about if simply looking at the website letters.
2) I got a mug few year ago, it's amazing as it turns color when filled with hot water, I loved it and used it a lot of time.
3) When I visited a factory, the factory boss invited me to try their fresh new teas, it's amazing, I liked the taste! Then when I left, the boss gave me a box of tea, I enjoyed it and recalled this factory quite often.
So, it seems people care a lot if the giveaway is really useful or not, if people love it, they will remember it for long. Of course, cost is a big concern, the fresh new teas are quite more expensive than a pen.
Back to the topic, I do not think pen is a good idea, as no much space to show your advertisement (a printed website is far from enough), mug will be better especially if the mug has some fancy functions or design. My suggestion will be to prepare different giveaways, try to guess which your customer really likes, and give the right giveaways to the right person.