I would hold off a little bit until you get clips/straps or go clipless. Let your body get used to the bike, to riding etc then consider an upgrade. The advantage of clipless systems is efficiency and reducing "hot-spots" on your foot. Basically, when you clip in or use toe straps you decide to not only push down on the pedals but to pull up (right foot pushes down, left foot pulls up---the basic concept of spinning) and are therefore being a more efficient rider. The other nice thing about clipless systems is that they require a shoe with a hard sole. The hard sole does 2 things: 1) helps to channel as much energy as possible into your pedal stroke (running shoes are not good biking shoes because they flex and absorb energy that would otherwise be transfered to your pedal-->crank-->chain-->rear wheel) 2) it also serves to distribute the force over the entire surface of your foot in order to prevent "hot spots". If this doesn't make sense try this experiment: have someone step on your foot with running shoes on then have the same person step on your foot with the heel of a pair of stilettos. Which one hurts more? Now consider that while you might be expanding the surface area by 4x for cleats you'll have that amount of force applied to the balls of your feet for a while. A small burning sensation will develop and you might even bruise your lil' piggies.
If you're set on binding your feet to your pedals (and are willing to rock the short but sometimes steep learning curve--by steep I mean that I've seen more than one person take a nasty fall at a stop light when they forget that they can't just put their feet on the ground) go for it. I'm pro-SPD (Shimano Pedaling Dynamics). I've tried SpeedPlay, BeeBop, SPD (there are various versions), Time ATAC and a few others and always been happy with my Shimano 858s (yes, I realize they're not made anymore but the 969s or whatever they are are even more bettererer than the 858s which were a step up from the 747s....on a side note, I wonder what Shimano will call their new pedals....)
You should consider float... Do you have bad knees? Do you walk funny (pidgeon toed, bow legged, etc). Most clipless pedals have 8 degrees of float which is fine for most people but there are some people that require more float so as not to hurt them there knees. Speedplay and BeeeeeeBop offer something like 20 degrees.
I think those eggbeater pedals are really popular now. I've never used them. They offer 4 different ways to get into them. Sounds good to me.
I hate straps. I think they're more dangerous. They don't offer float (when used properly), they're more of a PITA to get in and out of AND they're usually rocked by the same people that find it necessary to buy $80 Rapha bandannas. (Incidentally, Rapha is the bike world's equiv. of Hummer and therefore my mortal enemy!).
All that said, it's more important to get a good pair of shoes than a good pair of pedals. Pedals hold your shoes, shoes hold your feet---feet feel more pain than shoes or pedals. SOOOOOO go to a bike store after you've been on your feet for at least half a day--your feet will swell and you'll get more accurate sizing. Keep 1/2 - 3/4" space between your big toe and the tip of the shoe (your feet will slide forward while riding and the spacing will keep you from ruining painted toenails or even better, keep you from getting bloody toes). Different brands are made differently. Northwave tends to be 1/2-1 size bigger than Sidi and a bit wider. Carnac has a big toe box. Synthetic shoes don't stretch (cheaper Northwave and Sidi) leather shoes do (Carnac uses Kangaroooooooo!).
Whoa apologies for the rambling. I'm trying to rock drum scans while responding to this stuff.
Ask questions if this didnt make sense.
Time ATACS are the best. Thank you bike messenger for cluing me into them. So much better than SPD IMHO.