Fixies are fun because they are massively impractical, and demand a large level of physical ability and riding skill. They're challenging and look cool.
If you do not have a large level of physical ability and riding skill, you will park it in a corner and just look at it from time to time, wishing you were cool enough to ride such a cool bike.
Gears first, fixie when you're bored of gears.
If you live in a flat area (Florida, coastal Louisiana, Nebraska), a single speed looks just like a fixie and won't shred your ankles and calves and mess your knees up. If you don't live in a flat area, go for the gears.
Even in a flat area, I was breaking pedals, trashing BBs and cranks and pringling rear wheels on my single speed back in college (I was a 260lb clyde then). It took a while to gain the strength to tackle the inclines on bridges without walking, and a lot longer to learn how to modulate that strength so I didn't trash the bike. If I had the money, I would have gotten at least a 3sp. Looking back at how much I spent getting the rear wheel trued as often as I did, I could have bought a nice one.