It depends on what you want.
Bikes like the CG125, and YBR125 are best for starting off, cheap to buy, to run (LESS than 100mpg means somethings wrong) Cheap parts.
A CBR125R is a good choice as a first sporty bike, handles well enough for kneedown lean angles (I got my knee down on the CBR125R before my CBR600F, and RS125) and also gives decent fuel economy 70 mpg if thrashed, with the potential to do 150 mpg, if you try hard enough.
2 Strokes are very quick, but all are abused, and because they can be derestricted, you need to ensure that they meet the 15 bhp limit, otherwise your licence and insurance are invalid. Competion grade 2T oil is not cheap, and you should NOT run a 2 stroke racer on less.
You will drop your first (maybe even second or third) bike. Get a spares pile. There is no point saying I won't drop it. Everybody says that.
500 quid will set you up with complete fairing kit for a CBR125R, along with most bits that get broken with a drop, levers etc.
Once you pass the test, if you sell your 125 you will miss it.
Also, the DSA have a list of acceptable 125's for the test. It is a good idea to get one of those.
The chinese bikes quality is still suspect, so leave alone until they improve, but they are cheap, starting new for 800 quid for the lexmoto CG125 copy.
All things considered, it is best to get a CG125, or YBR125. You will find yourself getting a sports 125 though.
Insurance isn't as bad as everybody makes out.
a CBR125 is 260 quid to insure in lincolnshire, and my old scooter was 250 a year.
An RS125 will cost up to 500 in the countryside, more in a city.
(for a 18 year old, 1 year no claims)
Ultimately, bear in mind, no matter what the other guy says, it has been dropped if it is used. In all probability crashed as well, and is unlikely to be well maintained either.
CG125's start very used at 200 quid. YBR's about 800 quid, a CBR125 can be picked up for 400 quid, but mine was crashed badly by two of its owners (out of the four its been owned by) and the owner just wanted rid of it.
My RS125 was 200 quid because its owner hadn't realised you needed to pull the left lever in when changing gear, and ruined the gearbox. It has also been sized at least once, and was partially derestricted.
The standard market value of these two is nearly £3000 in total, so you can make money on your 125, but you WILL miss it.
If the 125 has one mature owner, riding since brit bike heyday, only used on sunny days out, with low miles, buy it. It will give far more peace of mind than any other 125, even a new one. (Fear of dropping your brand new bike)
Have fun. Everybody else did.
You can wheelie, get your knee down, stoppie, and do any other trick on a 125. doesn't mean you should.