You can do most projects with straights, and they come in a couple of lengths, so if you're feeling squished, you could try looking for a longer straight. And your work will scrunch up on the needle so you'll be surprised by how much you can get on there.
There are some projects that work best on circulars or dpns - bags, socks, hats, etc - if not for any other reason than not having to do so much seaming.
I use my circulars for most of my straight-needle projects now because I find them more portable and I love to KIP (knit in public). They also make it easier to work on larger projects like blankets because they tend to distribute the weight a little more evenly. I find circulars easier to work with than DPNs but....
Don't be afraid of DPNs! I haven't mastered them yet, but they're really not that difficult once you get the hang of them. These are good for socks and other small diameter circular projects.
I'm not sure what the best answer is on when a beginner should start using these other needle types. I was a "beginner" for a long time, and then just finally sucked it up and dove into some more difficult projects. I feel like I've learned more in the last few months than I had in the last two years! Just realize that every new technique is going to feel a little weird at first, accept that it might take a few tries and some , but know you WILL get the hang of it!