Is it a good practice to choose my undergraduate research topic on my own? Can I get enough help? (This question is one of three correlated questions: How should I do it? (second part), What are the downsides? (third part).This is the first part)

I am an undergraduate student (in Computer Engineering) and I will be starting undergraduate research for my thesis. I have talked with many professors about possible projects and all the projects they proposed to me seemed interesting enough. 

During summer, though, I read a paper and I was very interested and excited about it, but this paper was not for the projects that were proposed to me, but in a different area. I would like to do research in this area but I have some questions, because none of my professor is doing research in this particular field. 

So, my questions are:


Should I try to do a project in that area, even though my professors
aren’t doing research in that particular topic (some do research in a close field) or choose one of the projects that were proposed to me?
Will any professor be able to help/guide me through the project,
even if he is not doing research in this topic exactly? (I will ask
them if they are capable of helping me, but I want to know, how much
can someone help me if he is in the same field but I am doing
something different than his projects)


P.S. I want to understand whether it will be beneficial to do a project that I want to do because of some paper(s) that I read or it will be better to do a project that was proposed to me. Also, I would like to go for a Ph.D. after I graduate.
So somewhere I've made a moderators life harder, because I thought your three correlated questions were just one question. I think they probably could be, just incidentally. I'm going to answer accordingly, because when it comes down to it, How To Do It, Will I Have Help and What Are the Downsides aren't just correlated - they're interwoven.

My bias: I did my own projects. As both an undergraduate and a graduate student. This worked out quite well for me, but is not without it's pitfalls.


First, yes, your professor should be able to support you in your research interests - the odds of what your interested in being so far afield from their expertise, when you're an undergrad, is fairly unlikely.
That being said, there are two elements of support they won't have: infrastructure and funding. It's helpful, if you're working on a project, for there to be grad students and postdocs working on similar things. Code you can use. Helpful little suggestions like "Have you read Smith's most recent paper in Journal of Important Things?" That kind of ambient helpfulness isn't going to be there. Similarly, even if you're working for free, its way easier to justify conference travel, a piece of software, or an open access publishing fee if it helps an existing research project.


As I said, this worked out quite well for me - I got good publications out of it, and I got to work on my own stuff. But its a harder road, for graduate school may take longer, and you lack the security of working on an established project. Beyond that, if it doesn't work out well, you don't have an entire lab's worth of effort, papers that might be salvagable, etc.