Yes, a mailing list is important. It can be the difference between doing okay and doing really, really well. It's not easy to get subscribers and can seem pointless for a long time, but once you have even a small list, say a few hundred people, it can help propel a good book higher. It's a direct line to readers interested in your work. Anyone writing romance or erotic romance who doesn't have a mailing list is seriously missing out on a great, easy source of promotion.
A blog is fine, but if I had to pick between a site and a list, I'd pick the list. People like to feel special. When they sign up for your list, and you send them a new release announcement in a conversational tone, letting them know you're telling them first, it's a bit of a stronger connection than if they just read it on your blog. You have reached out to them in a different, more personal-sounding way. This is especially true if you offer occasional perks, like a Smashwords coupon for a backlist title, a free short story, anything that's exclusive to your list subscribers.
When you announce a new release, a percentage of your mailing list subscribers will buy it. That percentage is going to vary, but unless the list is really small, there will be some. The bigger the list, the more auto-sales from subscribers.
As your list grows, just sales from subscribers can push your book into the top 100 lists for the category and get it on the hot new release list for that category, which means more people see it, more people buy it, and on it goes. And you don't have to have a list of thousands (though the more, the better). Even relatively small lists of a couple hundred can provide a boost. It's a fantastic way to get visibility for something new. Who knows which book, if it gets on the right list in front of more people, won't take off? Give them all that shot.
And it's not difficult to set up a list, it's free many places, so there's really no good reason not to do it.
I will say that gimmicky ways of building a list are likely to disappoint. You need real subscribers who signed up because they're interested in your work. Prize giveaways can boost your list numbers substantially, and some might be interested, but I think the open, click-through and buy statistics on a list that's formed any way but organically is going to be a bit lower.
Make a list, put the link on in a prominent place on your blog, put it inside your books, and use it only to announce new releases or update people about once a month or so, maybe twice. Recommend other books they might like when you have nothing of your own to announce. Announce sales there first, maybe offer a free short story to subscribers, something like that.
Giveaways of a free story to entice people onto your list will result in a higher sales rate than a giveaway of a gift card or something that has nothing do with your work. But you don't have to give anything away, maybe just announce new releases there first, announce sales, and point out that your subscribers find out about things before anyone else.