As others have said, you cannot be British as British citizenship can only be passed down by parents who are British otherwise than by descent.
The family settlement route will shortly change and it will be much tougher to come to the UK as the fiance, spouse or dependent relative of a UK citizen or someone settled here.
Changes are expected in the summer that will set a minimum income level for sponsors of somewhere between £18,000 and £25,000. At the moment, all your b/f would need to show is that he has £105.95 per week left over after rent, council tax and utilities to support you without recourse to public funds. Obviously, he would need to find employment after he graduates to meet this requirement before he could sponsor you.
A fiance visa allows you to come to the UK to marry. After marriage you would have to apply for a spouse visa to remain in the UK. Until you have a spouse visa you cannot work.
The changes are also likely to lengthen the probation period before a non EEA spouse can claim indefinite leave to remain from two years to five years in line with other routes to settlement.
Other changes are likely to be made to toughen up the proof of a genuine relationship evidence required.
If these changes come into effect, the ancestry visa will be your best option. It will be cheaper and easier to apply for.
You only need to prove that you have a British born grandparent and that there is every likelihood of you finding employment in the UK.