You should be able to get a reasonable steak stovetop using a cast iron grill pan, if you have a strong enough exhaust. Oil the cast iron pan (with canola or such), then heat it very hot, until it starts to smoke. Make sure the meat is completely dry on the outside (wipe with a paper towel, water will prevent browning) and gently place in the pan. Leave it there for a minute or two (it'll smoke quite a bit!), rotate 90° to get the nice grill marks. Leave for another minute or two. Flip, and repeat for the other side.
It may splatter, have a splatter screen handy. It will smoke, quite a bit, make sure the exhaust is on high.
You will probably have a medium-rare steak now. Using a thinner cut will make it more well done (you can cut a thick steak in half with your chef's knife, making two thin steaks); so will plopping it in the oven (not sure if you want the oven before or after searing, I like 'em medium rare...).
Remember to let the meat rest for 5 minutes or so before serving.
Also, if your steaks are coming out ridiculously tough, you're probably using the wrong cut of meat, or some terrible grade. What cut are you using?
[edit: I should note that, in case it wasn't obvious, the burner should be up pretty high]
Edit by rumtscho There is a reason this answer specifies a cast iron pan. If you are limited in your cookware choice, pay attention to the maximum temperature your pan can tolerate. If you are using a non-stick pan, you have to go on medium heat and wait longer, else you'll damage the pan. (And sorry, but you can't get it as tasty as on high heat that way).
It is absolutely worth adding ground pork or veal. I usually use a leaner ground steak and compensate with a fatty ground pork (shoulder is good) - fat = flavour.
Another tip is to take your time. Many people try and cook bolognese in half an hour, but considering ground meat is usually made with tougher cuts, you end up with tough meat and under-developed flavours. Use plenty of onions and garlic, brown your meat well, use good wine, stock, tomatoes and herbs (thyme, rosemary and bay) and gently simmer that bad boy for at least 3 hours. For ultimate flavour, cook it the day before and let the flavours marry overnight.
Best Answer
There is no single cut of meat that is universally used in Philadelphia. Top round is common, and it may actually be the most traditional given the sandwich's Italian origins (top round is what is used in braciole and Italian beef sandwiches). It is becoming more and more common to use rib-eye, though, which is what is used in some of the most popular Philadelphian establishments (e.g., John's Roast Pork and Tony Luke's), which makes sense given its higher fat content.
As lazoDev mentioned, you should be able to get your butcher to slice the meat into thin (~1mm) pieces. If that is not possible, though, you can put an entire rib-eye roast into the freezer for a half hour or so. This will harden the meat without actually freezing it solid, and will make thinly slicing by hand much easier.