Yes chickens are flock animals and as such need to be in a flock. I personally would not recommend getting less than 6 chickens but if pushed I would say 4.
Not only do they need eachother for company, they huddle together for warmth.
Chickens have a special dynamics to their flock, a social order. You need more than one chicken to do that, you need more than two chickens to do that.
I started out my flock with 12 chickens and added more shortly after.
Don't be surprised if she never lays a single egg, hens that are depressed or stressed will not lay, some will not eat and then eventually just give up and die.
Before it gets to that point they usually turn nasty on you, not much of a pet then.
The only people I have ever heard of that raised a single chicken and it lived were the ones that had house chickens, yes a chicken that they raised in the house like a dog. Personally I think its disgusting but hey whatever, but the only reason why the hen was okay was because it was around people all the time, not left outside alone.
I would be very surprised if a feedstore would even sell you one chick, all the ones around here have a policy of no less than 6 and for the reason I described above.
Ever see on chick all alone in a brooder cage chirping over and over because its lonely?
I see people all the time on the chicken forums asking for help because they have one chick survive out of a hatch and they don't know what to do because its screeching, won't eat or drink etc. because its so lonely.
The advice given is always the same, get more chicks for it, they need friends.
Aside from all that, I don't know how you would make a decent safe run out of tomato cages but keep in mind that predators can burrow under anything that is not in the ground a couple of feet deep and if you don't have a roof on it you can expect a problem with hawks or if you have chicks then even crows will be a problem.
Also, the weather is not right for chicks right now. You need to keep them in a brooder for a few weeks inside the house or a garage that is warm enough for them before they can go out.
If you get some now then you should be putting them outside by late feb/early march, which is still pretty cool for a young pullet. That is the reason many people don't do them this time of year.
Keep in mind that you will also need a brooder, with lights and feeding dish and waterer before you ever need a coop.
Chicks do not go right into a coop, make sure your parents are okay having chickens in the house for a while.
Do you know if you need a permit to raise poultry in your town?
Many people do, myself included. If you get chickens without a permit and you are suppose to have one the town will force you to get rid of them.
Even in the country where people assume they can do whatever they want alot of people are shocked to find out that a neighbor reported them, the town or city comes out and gives you 30 days to get rid of all of them. Call your local board of health or animal control officer to find out if you need a poultry license before you do anything.
See if your parents will help you build a proper coop, it does not have to be large and expensive but it should be safe and comfortable for the hens.
I know you are excited to get chickens and I hate to be a drag but please give this alot more thought.
Take it from someone who has alot of experience raising and breeding chickens, there is alot to consider and you need to be fair to the chickens and yourself, you will have alot of headaches if you do not prepare for them appropriately.
That said, I do hope that you can go about it in the right way and eventually get your chickens, they are a great deal of fun and you can't beat having fresh eggs.