What features should I look for in a fireplace grill?

Your primary features should be:

1. Safe design. This means the unit should remain steady when engaged with the fireplace.
2. The ability to easily add and remove food from the cooking surface.
3. The ability to easily move the cooking surface closer to and further from the fuel source.

These are paramount. Your first priority is to do no harm, so you want a stable grill built for the purpose of hearth cooking that won't fall out of the fireplace and set your apartment aflame. The ease of use is also important (and is probably a contributor to overall safety), as you want to be able to control your cooking conditions without much complication.

As a secondary concern, I would want something that either had a rotisserie option built-in, or was rotisserie-capable. Also, I'd want maintenance to be simple. The default thought might be to go for cast iron, but you should consider that it will likely be facing temperatures that will kill the seasoning, and reseasoning could prove to be difficult. So it may be worthwhile to do some research on the best material to use for the long term.

This won't be a direct answer regarding the grill, but a popular alternative:

Consider getting a cast iron dutch-oven and a wire/metal bbq basket instead.

Cooking over the open wood fire is akin to driving a rocket through a go-kart track. Most people burn the logs util they have have built up good amount of charcoal. At this point, you either bury the cast-iron pot in the coal or place the cage containing food over the charcoal and watch the magic.

a couple of small blocks of stone/brick propped on the desired side usually leads to the perfect height of the cage over the coal. Best part is that the cage and the pot fit in the sink for a quick cleaning.

here is a cross section picture of the cast iron pot in coals. From Modernist Cuisine, Nathan Myhrvold:

I'm mostly a reader at this site, but in this particular case, as an Argentinian barbecue fan that used an indoor grill for many years, I feel somewhat qualified to spit out some warnings:

• Use embers, not direct flame. The flame will burn your meat.
• Temperature: you should be able to hold your hand for three seconds just over your grill when cooking, no more, no less. You may use an adjustable height grill or just adjust the amount of embers, as you prefer
• No greasy meats. They'll clog your chimney after some time and leave grease at your fireplace floor (the smell is nice while cooking, but not afterwards)
• Be sure your chimney works very well before attempting to use a grill indoors. The smoke smell may last for a week on curtains and mats
• NEVER use it to cook fish unless your SO is a seal

(more on some desirable grill features later, need some spare time)