There's so many things you can start seeds in. The wet-kitchen-towel-freezer-bag method is only recommendable for beans and peas... things with big 'seeds', so you can count out the ones that aren't going to sprout. Still, I'd definitely recommend planting right in soil. I've been experimenting and started seeds in a number of different places and ways. The ones I used the bag method on are a lot slower than the ones I've had in my windowsill propagators. I would advise you get at least one of those, they're really great! They don't have to be heated, just the cheap kind, I only paid £1.99 for mine at QD. I've got them in my east and west windows and they work great, solid results within days. They're good too because they come with a watering tray so you can water them from the bottom.
Another good thing I have is watering trays with capillary mats. They're a bit pricier at £4.99 for two of them, but I just sit little peat pots on them (from the 99p store) or those expanding peat pellets and water from the bottom also. You can also use egg boxes or toilet rolls with one end cut into strips and folded up to make a bottom.
I wouldn't put anything outside this time of year until it's at least a foot tall, and even then I'd put it in the mini greenhouse. Those are great also, I got mine for £7.99 from QD and I'm thinking of getting another because I got the three-tier although I would advise getting the four-tier - better value, uses the same amount of space but you get more space inside it.