You need to have an idea what sort of result you want to achieve (roughly what size, how natural etc) and then go and see some surgeons. If you see good surgeons, they will advise on what to go for to get the look you want, what size/shape etc will suit your body frame etc. You should see several different surgeons, so you can compare what they all say/reccommend.
The best place to find a surgeon is to either go to your GP, who may know of an NHS one in your area that does private work also (most do) or to look on the BAAPS register for plastic surgeons. At minimum the surgeon you use should be on the GMC specialist register for plastic surgeons, but they should preferably be on the BAAPS register too. They don't need to work for a big company, many are independant and work out of local private hospitals. If they work in the NHS also, that is a good sign. You also need to find a surgeon that specialises in breast surgery.
If you go with a big company, you will get a free consultation with a surgeon (although if I remember correctly, Harley Medical Group don't let you see a surgeon without paying a deposit, at least they didn't used to, you see a 'nurse' (salesperson) first) but you are likely to get less choice over the actual surgeon you use, unless you request a specific surgeon by name. You will also be likely to get a lot of 'hard sell'. Most companies also charge for 'aftercare', which includes post op care and repeat surgery if something goes wrong. That said, big companies are very popular, easily accessible and the surgeons will often be very busy, so have lots of experience. Try and look into the actual surgeon though if you can. After all, it is them that will be operating on you, not the company as a whole.
If you go via your GP's reccommendation or find a surgeon yourself on the BAAPS register, you will have to pay a consultation fee, but will get a much more comprehensive consultation and maybe a more qualified and experienced surgeon, although that's not always the case. You will also get to choose your actual surgeon. You won't pay for 'aftercare' with these surgeons, but they will usually re operate for free if needed, although you may have to pay theatre fees.
Neither option is routinely cheaper/more expensive.
Things can and do go wrong. You need to think about whether wanting larger breasts bothers you enough to risk serious disfigurement. Even with the best surgeon things such as infection can go wrong and leave you with serious scarring and problems. The anaesthetic is also a risk, although some surgeons offer the surgery on a local with sedation now. The risks are small, most surgery goes without problems, but the risk is still there and does need to be seriously considered.
Hope this helps. If you google you'll find the BAAPS site and there are also some specialist cosmetic surgery forums. Let me know if you want to know anything else.