Just as a general point first of all, not many people who haven't been through an immigration process have much of an idea about what actually happens. In the UK, as in most countries if not all, you need to become a legal resident first, and then apply for citizenship some time down the line. To find out about the immigration stuff, go the Home Office website (google it...).
To join NATS, you need to be between 18 and 36, and have the right to live and work in the UK - that does NOT mean citizenship. There are a few Irish ATCOs in the UK for instance, who will never take citizenship! They don't need to in order to work there, as they are EU citizens.
You need to be able to obtain a Class 1 medical certificate (as opposed to the Class 2 or 3 needed in most countries) to be a radar controller in the UK, and you also need to be able to obtain security clearance. There is nothing you can do on your own behalf for that clearance - you just submit the forms and cross your fingers.
Back to the immigration side of things, no occupation is "special enough" for citizenship, though there may be some which help with residency. Check the Home Office site for that info. Being a septic won't stop you being considered for ATC, so long as you have the legal right to work in the UK, which you most likely won't get just by applying to ATC.
Your degree won't be particularly helpful beyond the fact that it shows an interest in aviation and that you're not an unemployed bum (personally I think everyone should spend a few months every few years as an unemployed bum - great for recharging the batteries!). You'd still have to start from scratch on the basic ATC course. As to whether you'd want to...
In terms of what to expect from your lifestyle, UK v USA, the following sums it up:
Housing costs in the UK are MUCH higher.
Taxation in the UK is higher.
Get used to the idea of paying $8 a gallon or more for gas (that's in little US gallons before I get shot down - 1 US gallon = 3.8 litres).
Cars are much more expensive in the UK.
On the plus side, you're still less likely to be shot in the UK, though your car has a greater chance of being stolen!
You can expect to work a regular 6 on, 4 off pattern in the UK, with 6 cycles of leave per year; much better than in the US.
You cannot work more than 2 hours (or 1.5 hours in some units/sectors) without a break in the UK.
My suggestion would be to do more homework (you could have websearched much of what I've just typed - lucky for you I'm bored right now) and if you still have a way to go in your studies, investigate the possibility of spending a summer in the UK between semesters. There is an exchange scheme which allows British and US students to get temporary work visas in each others' countries.