You can go either route. Historically, most accounting majors went to work for an accounting firm because becoming a CPA required you to have a certain number of years of audit experience to get your license. The trend now is many states are eliminating this requirement, or creating a separate class of license that does not require it.
Some companies, especially larger, publicly-traded companies, have Internal Audit departments, which will allow you to get signed off for your audit hours. Some companies will allow you to do a rotation in internal audit even if you don't work in that particular department so that you can meet the experience requirement for your CPA.
The current environment is hard on CPAs as well as anyone else. Even if you aren't laid off, you may have limited ability to be promoted or limited salary growth. I don't think any job is truly "recession-proof." Accountants can and do get laid off, and of course if a company goes out of business, everyone loses his job.
But they generally are the last to go. During the 2001 recession I was working for a large insurance company, which had a 20% company-wide headcount reduction. This was quite big news, as the company was a major employer in the area. However, the finance and accounting departments continuted HIRING during this period. When times are tough, the CEO wants the month closed in one week instead of two. He wants budgets revisited quarterly, and then monthly, rather that just annually. He wants much more detailed support than he wanted before. All of this increases the workload of the finance and accounting departments of a company.
Many people are surprised to hear that, in spite of its nearly total shutdown in early 2002, Enron continued to exist until 2007. It existed as essentially a shell company whose main purpose was to liquidate the assets that the company had previously held. I can guarantee there were still a large number of CPAs working there, possibly even more than when the company was operating normally prior to 2001. Throughout this period, the company would still have been required to prepare financial statements, forecasts, SEC filings and tax filings. In fact, the increased complexity associated with discontinued operations, and the increased regulatory scrutiny of the company, probably INCREASED the workload of the finance and accounting departments.
You are also correct that you don't have to start all over again if you are laid off. When and if the accounting manager at ATA or Aloha is laid off, she won't have to start over again as an entry-level accountant at a new company. She will be able to get another comparable position at another company. And most CPAs are able to switch to different industries. CPAs do specialize, but it usually is by the finance function, not the industry. A CPA who specializes in SEC reporting or tax or internal audit will be able to get a job in that department at a different company, even if the company is in a completely different industry.