Publishing is somewhat difficult for an undergrad as you can't really get published unless you have something original to say/add to a domain of knowledge (that's the whole point of a PhD). Finding the time to research something original while doing undergrad work is something I didn't even think was possible, the last thing you want is a reputation for trying to publish utter crap.
Because it's rare for undergrads to have research experience, it makes a big difference in grad school admissions. The admissions committee guesses how good a researcher a student will be based on grades, test scores and professor recommendations. If the student has actual research experience, there's less guessing to do.
A lot of professors have smaller projects that are part of their overall research that they can give to undergrads to do.
But, this isn't really helpful to you now. Your question is really "What are my chances?" and I can't tell you. For the people at the top and bottom, grad school admissions is easy to determine. But for those in the middle (I was one of them), it's almost random. Like many things in life, now that I've been through it, I know what I should have done.
If you want to go to grad school, then apply. Not applying is a 100% chance of not getting in. But try looking for schools that do research in what you're interested in, and look at schools outside of the top rankings.
There's no harm in applying. Several students in my PhD program took a year off after undergrad and worked in a university research lab as a paid assistant. Some said that they got into some grad programs after university, but they wanted to get a better research background that would help them get into a more prestigious school.
I suppose it's too late now, but to really distinguish yourself for some top-tier universities, you'll probably have to show evidence that you've pursued research or self-study (e.g. summer programs, indep study/research classes with a professor, personal projects, internships, etc.).
From what I've researched it seems universities are only interested in your undergrad or masters degree. High school and college stuff doesn't count (I'm in the UK).
