Electric coil is safe on just about every cooking pot/pan you can buy. It's just another heat source.
If a pan has a special requirement, it will say so on the packaging before you buy it.
Regarding a pan to sear meats, you can do no better than a good cast iron pan.
Cast iron will retain it's heat even when you drop a slab of cold meat into it. This makes for better, more even searing. To make things even better, you can then take the entire cast iron pan and stick it right into the oven! No other pan needed.
Personally, I cook steaks in a cast iron pan like so:
1) Take steaks out of fridge and set somewhere to slightly warm up while you prepare everything.
2) Put cast iron pan in the oven and turn it on to 500 degrees F. This will heat up the pan while your oven pre-heats.
3) On a plate, add a small amount of oil (canola or vegtable, not olive oil - you're going to be using very high heat, so you want a high smoke point). In a dish, add Kosher Salt, and pepper and mix around.
4) Put steak on oil plate and turn over a few time to get a light coating. Sprinkle salt/pepper mix to your liking (I personally go overboard on this).
5) Take the pan out of the oven and put it on your stove. Turn on your largest stove burner and set it as high as it will go. Put your pan on this burner to continue heating up.
6) After it's very hot (test by dripping a very small amount of water, it should sizzle and evaporate almost instantly, your coils should be red in color), drop the steak right into the dry, hot pan and don't touch.
7) Let the steak sear on that side for 30 seconds. Flip it once and let is sear on the other side for 30 seconds.
8) Put the entire thing into your oven. Wait for 2 minutes, take it out, flip the steak and put it back in the oven for 2 more minutes.
9) Take the steak out and put it onto a plate with a smaller plate or bowl turned upside down. This makes a slope for any liquids to slide down, away from the tasty seared "crust" you've developed. Cover loosely with foil. Let rest 10 minutes before cutting (very important to keep the juices from spilling out).
10) Enjoy your medium-rare steak!
You can adjust the timings a bit depending if you have a particularly thick cut of steak, or prefer a different doneness.
Be very careful with the cast iron pan, as it will retain it's heat for a long time! Also make sure you use proper care for it, since taking care of your cast iron is a bit different from a normal pan. If you take good care of it, it should last you a lifetime without issues. Some people even hand down their cast iron to their children! Here's some good information: http://www.epicurious.com/expert-advice/how-to-wash-season-and-maintain-cast-iron-cookware-article
