There's two major things the other answers don't address so far:
A manual drill is much harder to use than electric drills.
A manual drill requires two hands to operate, which means you need a way to hold whatever you're drilling into steady. It's also hard to keep it straight since you're drilling for so long, so especially with smaller bits you're more likely to snap them.
I'd also echo what Michael Karas said: the experience of a manual drill is so different from using an electric drill that it's not going to give you a good feeling if you like doing that kind of work or not. In fact, I'd suggest that you'll decide you hate drilling because it makes your arm sore and takes several minutes per hole, and not like DIY as a result. For me, I like DIY because I like building things -- I don't dislike drilling holes, but it's not about that.
Drilling plastics and concrete are two different requirements
You can purchase basically any electric drill and be able to drill plastics. Cordless is quite convenient and definitely can do the job. If you go cordless, personally I'd recommend sticking to 18V+ tools (although some of the big name brands make decent 12V tools). Keep an eye out and you're likely to find a starter drill/driver for under $50, and it's one of the basic tools that's useful. That said, don't expect a cheap drill to last several years, especially if you end up using it a lot.
Drilling concrete is a different story. You can get by with a normal drill -- if you don't mind spending several minutes per hole (and if cordless, using up batteries VERY quickly). However, the most effective way to drill holes in concrete is with a mains-powered hammer drill, and you can also get cordless hammer drills.
In my experience, I have a decent cordless hammer drill, but I only ever use it for small (concrete) jobs, as the battery wears down fairly quickly when going through concrete. The upside is it's a great all-round drill/driver, and can tackle basically any type of job. My corded hammer drill is probably 3 times faster and can keep going all day, but is not very easy to keep at low speed, and is harder to use for precision work since it's relatively big and heavy compared to a cordless drill.
- If you want to drill plastics only, look for a sale on a corded or cordless drill (and in fact, I'd recommend cordless in most cases)
- If you want to do small concrete jobs AND plastics, you could get away with a (more expensive) cordless hammer drill or maybe a corded drill with very good variable speed controls
- If you want to do medium/large concrete jobs AND plastics, buy two drills: one cordless (for plastic), and one corded hammer drill