i don't think movies are always a bad idea--provided you do dinner
after the movie. by the time it is over, you aren't so nervous since you just spent a couple of hours next to her (plus you find out if she's the annoying type of person who talks through the whole movie!). and it gives you something to talk about if you are worried there will be a lot of awkward silences.
i think your picnic sounds fabulous. it's not as standard as the movie--which is always a nice change!
if you don't want to come off as desperate, well, i don't think i'd start mentioning anything about a long term relationship to her on the first date
and i also wouldn't mention that this is your first first date--you shouldn't pretend to have more experience than you do, but there's no reason to make her wonder why you've never dated before. if things progress, bring it up later in the relationship
waiting a couple of days does nothing. if i am anxiously awaiting a call from a guy because i'm excited about seeing him, when he doesn't call for a few days it leads me to believe he's not as interested. that doesn't make me more interested, only less. at the same time, no one wants a stalker--so unless you got a very strong vibe that it was an amazing connection from her side as well--i'd suggest waiting till at least the following day.
i'd stay away from icebreaker type games. it's a date, not a game show. play mini golf as someone else suggested, or take a frisbee or ball to kick around if you'll be in a park like area. but regular old conversation is the best way to go. if you know some of her interests, looking into them a bit might make for a more interesting conversation. plus, it's flattering a guy took the time to know a little something about what matters to you. (and the questions you ask are going to be much more intelligent as well)
for me, a first-date has always been enough that i knew if i wanted to get involved with the guy or not. some people need more than that, but in my experience one is enough. from then on i know if 1) i have no interest in seeing this person ever again, 2) they aren't someone i'd get involved with, but we had fun so going out with only that expectation is a possibility, or 3) there's definite potential for a relationship.
good luck, have fun and be yourself