Once you've categorized everything, make sure you purchase everything in the first category before you go on the the second, and so on. By doing this you will soon become self-sufficient, from a backpacking point of view. What this means is that whenever possible, buy a product of good quality that will last. Otherwise, you will only end up replacing it before you wear it out and, in the end, spending more money than if you had simply purchased the higher quality product first. Rather than being completely subjective, and providing a list of manufacturers, roughly ordered by level of quality, I will just point out specific features one should keep an eye out for when shopping for particular products.
Tents do a couple of things that are, at times, contradictory with each other.
They keep you protected from the elements, and they keep you comfortable across a range of temperatures. Some tents are not suitable for all backpacking trips. What many manufacturers optimistically call a four-season tent is often too poorly ventilated to provide comfortable sleeping in the summertime. Many three-season tents are just that, tents that are suitable in spring, summer and fall. Assuming you are buying your first backpacking tent, it is likely that you will be looking primarily at three-season tents.