Lumpy idle, bit of a misfire and exhaust popping more than usual

Yes, a misfire "should" trip a "check engine" light. I would try an ECU reset first. Procedure can be found in your owners manual or here on the forum.

 

How many miles and when were plugs and coils last changed? Follow the suggestion above, and then I would look into replacing the coils AND plugs. Fairly easy to do and coils can be had on eBay from a UK seller for around $380 for a set of 8.

 

Few questions.

1. When was the car previously used? Has it been stood up a long time?
2. Does it have any modifications such as sports cats, sports exhaust, a remap?

If its a bit rough, try going out for a drive and filling some fresh fuel. The injectors may be a little dirty/clogged through lack of use, the fuel in the tank may have lost a little octane, etc.

Definitely do a battery reset, it will force re-learning. I always turn the key to keystage 2, wait for the check ok to go off and then depress the throttle to the stops (with engine off). This promotes a faster re-learning process as the entire throttle pedal and throttle body openings are all re-learned. You should be able to hear the throttle bodies opening and closing as you press the pedal to the stop and release. Once done a couple of times. Turn off again, then back on again and you'll find the engine re-learn is accelerated....

 

battery, coils and plugs.
So cheap. If you’re worried about splurging on these things on a 15 yr old car, this isn’t the car for you, respectfully.
Even if the coils and plugs aren’t the source of your problem, your car will run better with new ones, heck, you may even recoup some of the costs in gas savings,
Plus, very DIY.

 

Check the voltage supply to the ignition system before you start changing bits. If the volts are down this might effect the rest of it

 

Change the coils and plugs.