I want to start doing 30-40 minutes of cardio 4-5 times a week. Is it better to jump right in to jogging, or should I start out walking and work my pace up to a jog?

I think you'll find that if you haven't been active before there is no way you'll be able to just leap into 40 minutes of jogging w/out working up to it.

I've been working out seriously for 2.5 years now and when I started training for a 5k about a month ago, *I* couldn't run for 40 solid minutes. And I think I'm in pretty decent shape, all things considered. I can go at a pretty high resistance on the elliptical for an hour w/out a problem. I can lift weights, I can ride a bike for an hour ... you name it. And I still am having to work into running for a solid 30 minutes. I've been doing the Couch to 5k program and after 5 weeks, I"m up to running for 18 minutes at a time, and it kicks my ass.

What I've found has worked for me is the incremental build up to running that this program gives me. It starts out with walking for 1 minute and running for 1 minute .. keeping that up for about 20 mins. Then you go to walking for 60 secs and running for 90 secs ... keeping that up for 20 mins. Etc.

Take it slow and work into it. Don't try too much and burn out or injure yourself.

Okay I recently started running and I was fairly fit when i started, and jumped in starting at 6km runs in the morning. Now problem came when i got shin splints. After much research I found the best way to start, no matter how fit you are, is to do power walking as well as running.
The reason is this. When you jog you build up muscle at the back of your calves. You foot lands in a way which slightly twists it, which is fine unless you are doing repeated pounding for many miles. Having stronger calf muscles tend to make that more prominent and hence the shin splints.
If you power walk, or walk on your heels with your toes lifted lots, you strengthen the muscles at the front of your shins, which balances the leg more so less impact and less injuries.
Get some decent shoes off the bat, and try to run on the grassy verge rather than the concrete also helps avoid things like this. Trails are also excellent.

Increase the distance by 10% each week only, this can be painstakingly slow at first, but its worth it.

Try the couch to 5k program for a reasonable starter, it has walking/running combos to start you off.