We've looked at Selenium and Telerik and have settled on the latter as
the tool of choice due to its much more flexible recorder
I'm not sure how much you've looked into it. There certainly are other options as well. Have you looked into Watir, WatiN, Sikuli to name a few?
and we don't really want testers writing too much code.
I feel bad for the people who have to maintain these scripts. Most often, without code that can be easily modified, scripts become fragile and it begins to take longer to modify the script than it does to re-record it, which wastes even more time.
However, I am trying to understand the overall benefit. What are
peoples' views and what sort of things work well and what doesn't?
Test automation is a beautiful thing when done correctly. It saves time on regression tests/checks so as to give your testers more time to do what they do best, test. Don't believe for a moment though that it is a silver bullet. Automation scripts require significant time to develop if the application already exists but the tests don't, and require constant updating with each release. Automated tests are also a great way for new people on the team to see how the system is supposed to behave.
Also, make sure that your testers get to decide what needs to be automated. If it's a small check that doesn't take much to check, is very monotonous, and easy to automate, start with that. Always start with the checks that gain the most through automation, and work from there.
So far the main benefit we can see is for regression testing,
especially across multiple client deployments of our platform.
It is the main benefit, and if set up correctly, can test most of the browsers that you would need with a small configuration change.
We "think" it is the right thing to do but in an already busy schedule
are looking for some additional insight.
As I stated earlier, test automation takes considerable efforts, however, when done correctly, I haven't met a team yet who said "I wish we hadn't set up our test automation."