You'v set your boundaries pretty wide; street/food/landscape. I enjoy street and photojournalism, for this I wholly subscribe to the 1 body and wide lens philosophy, for a straight portrait I may use a 50mm, but i like the wide angles. I have a friend who is a successful landscape photographer, and he uses a load of kit; tripod, big, very expensive filters, cable release, a variety of lenses, but usually wide and ultra wide angle. For food photography, what are you thinking? Street vendors, restaurant plates and presentation? I know nothing about food photography, but i do know those who do presentation plates use flashes and soft boxes and a load of other bits and pieces.
Can all this be done with a body and two lenses? Probably, with a creative approach. Will you be able to produce the quality that will not only be taken on by agencies, but also sell? Well, you can try. Most of these stock sites only pay pennies if an image is sold anyway. For the agencies that pay real money, the barrier to entry is high, they require a consistently high quality of work.
Be aware that if a person is in the image, for commercial use you will need a model release. No release and the image can only be used for editorial purposes, making it a much harder sell. Of course, you may find yourself in the middle of a spontaneous, violent protest that is being broadcast on the BBC and CNN, in which case you could probably easily sell your images directly to media outlets. But this situation would increase your kit requirement to include at least a gas mask and probably a stab vest and a good insurance policy that will not refuse medical cover because you were in such a place!
Having a website is OK, but you need to try to make a name for yourself to get traffic and people looking at what you have to offer. You need to get in on the Facebook and twitter marketing stuff and submit work to competitions and publications to try to get some exposure. Without this the only people who will see your site are friends and family.