If by "personal" you mean a site that's not going to experience a lot of traffic, then yes, you'll find DH to be a very comfortable place to do all that and more!
If carefully coded and cached, a regular shared hosting account can still be good for a moderately high trafficked dynamic site.
You might even be able to host a high traffic site if it were static and didn't have massive amounts of media downloading going on.
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They're Dreamhost coupons!