+1 to @duffymo's advice. Hibernate is really a whole other beast, and it is especially difficult for folks who are so used to code straight-up SQL to switch to an ORM tool. I mean it took me awhile to be comfortable with Hibernate to do all the work for me, because I just didn't trust it will do a better job than my 'awesome' SQL code. But, as time passes by, I learn to accept that Hibernate is doing a fine job PROVIDED you configured it properly. :)
So, @john, I'll start with JSP + Servlet + Spring first, just like what @duffymo mentioned. Convert your DAO classes to use Spring's JbcTemplate. This forces you to create interfaces for your existing DAO classes. Make sure your DAO classes are stateless, I mean, it should be though. With that, you can easily test the crap out of it in your testcases.
For your servlet to utilize these DAOs, you need to do something like this...
ApplicationContext ctx = WebApplicationContextUtils.getWebApplicationContext(servletContext);
SomeDao dao = (SomeDao) ctx.getBean("someDao");
dao.doStuff(..);
The reason for that "tad ugly" code to get the DAO is because Spring cannot wire up the DAO directly into your servlet because Spring doesn't manage your servlet at this point.
Once you get all of this working, you should have some understanding on how Spring's IoC works. Now, you can swap out your servlet and replace it with Spring MVC. I suggest you use Spring MVC 3.x so that you can build your web part the restful way. Trust me, it's whole lot easier and cleaner than Spring MVC 2.x, in my honest opinion.
Okay, when you have JSP + Spring MVC + Spring + JdbcTemplate working, I think it will be a good time to swap your database module from JdbcTemplate to Hibernate. Since you code by interface, it will not cause ripple effects to other modules. PLUS, you can reuse the exact same testcases to test the crap out of your Hibernate DAO classes. Sweeet. :)
... and that's how you end up with JSP + Spring MVC + Spring + Hibernate. :)
Breaking this whole thing down into smaller chunk makes it whole lot easier to learn and digest. At least, when things start breaking in development, you won't indirectly improve your swearing vocabulary, trying to figure out the problems.