I raise anywhere between 50 and 100 Cornish or Rangers at a time, a few times throughout the year.
In your case, it is not unusual to purchase day old chicks from such places and lose one or two. They may have an isolated illness before you even get your hands on them or they somehow experienced an unseen physical trauma. If you order from hatcheries, they usually give one or two extra chicks in their shipment in the case one or two die in transit. This is not the case with stores like Agway or Tractor Supply.
When applying a heat lamp, make sure the chicks have enough room to get away from underneath the lamp, should they become overheated. Otherwise, it could be the heat lamp that does them in.
Red Rangers are a very good breed for meat but they usually take about 12 weeks to gain the size you might look for. Even at 12 weeks, they do not match the look of the little butterballs known as Cornish Cross Rocks. With the Ranger breed, you can save money during growing season as these are very adept at foraging for themselves while you supplement with the feed you give them. I also realize you said you have limited space, soooo...It turns into a trade-off... Rangers, with room to range, in 12 weeks at a dressed weight of 4.5 to 5.5 pounds. Or raise the Cornish sitting at the food trough, ready in 8 weeks at a dressed weight of 5.5 to 6.5 pounds.
Cornish
can be more prone to illness, especially with conventional feeds. I always maintain a clean coop and make sure they have fresh, clean water. If you feed them the recommended industry standards of high protein percentage feed (20 to 24%), you will want to eventually remove that feed from them for 12 hours at a time... once they are at a point where they do not need a heat lamp and can spent the night without light. Otherwise, you may experience mortality due to fluid buildup around the heart. We lost a few this way. They became even more lethargic than usual, accompanied by rapid breathing. One even presented with discoloration of the wattle and comb. Not knowing what happened, we performed autopsies and found them all to have fluid buildup around the heart. This led me to do more research on feeds and I discovered the "12 on, 12 off" recommendation for conventional feeds. But I found more information...
It is not so much the protein amount that is important in raising the bird. A healthier approach is trying to find a local feed mill that might produce a natural (not organic) broiler blend of 18 to 19% protein with an equally important amount of amino acids, biotin, and the other minerals necessary to healthy growth for these breeds. Remember, these birds are bred to grow abnormally quick and therefore
should have a diet specific to their breed. I also believe in staying away from any feed that contains "animal byproduct". Chickens will eat worms and bugs but I leave it to them to find that... I do not trust the label of "animal byproducts" because you can't verify what that is... but that's just my opinion.
For anyone living in the country, I would also recommend you take a look at "maggot feeders for chickens"... it's not as bad as it sounds.
What I feed my birds in three phases is Starter for 3 weeks, Grower for 3 weeks, and Finisher for 2 weeks. I have not had to introduce medications at all and not experienced any mortality since I began this approach. I am lucky enough to have Keystone Mills, in central New York, to provide these feeds. I get the feed through Round House Mills in Cortland. Another surprise I found in this journey is that the feed I now use is substantially cheaper than anything I can get at Agway, TSC, or Tractor Supply. Unfortunately, they are limited to central New York. You will have to do some research to find what is near you if you choose this approach.
Good luck and best wishes.