There are some gluten-free soy sauces out there, just look at all the labels!
I'm vegan, I dropped gluten back in December, and I've recently been eating on a very tight budget planning for a house purchase and a wedding in the next 2 months.
One thing I gotta tell you, drop the bread. Trust me, as far as I know, there is no GF bread out there that isn't about twice the price as regular bread. No longer relying on bread is something I have just had to come to terms with. If you have a birthday coming up or you can wait until xmas, you can ask family and friends to pitch in and get you a bread maker. By getting just the raw ingredients, and in bulk, you could save a bit of money. But until then, I would say, just drop the bread.
There are quite a few pasta alternatives out there. I have found: rice, corn, and quinoa pasta. But these are often a bit pricier too. Which brings me to my biggest tip: gravitate towards UNprocessed foods. Processed foods will almost always be more expensive, and are more likely to have random ingredients, such as hidden wheat or soy, or animal products.
My staples are the following: bananas, rice, corn, potatoes, quinoa, split peas, and lentils. I literally *live* off those! (and they're pretty cheap too!) And then I supplement every week with a handful of fresh produce: salads, fruits for breakfast or snacks, fresh salsa to use as a condiment, steamed veggies as a side dish, etc.
You learn to enjoy the natural flavours of food, and you learn to get creative in the kitchen and use spices and herbs, which I find is a lot of fun! Sweet potato+carrots, pureed into a soup? Yummy! Cheap, filling salad dressing: white navy beans, squeeze of lemon, dash of dijon mustard, black pepper=delish!
PM if you want more ideas or examples of what I eat! Good luck