I would estimate the total costs as somewhere from £1,000 to £3,000.
Stamp duty is indeed 0% below £125,000.
It's 1% of the total house price in the range £125,000 to £250,000. There was a temporary exemption for a while for first-time buyers, defined as never having owned a house before. That's ended now, though.
You need a survey of some form when buying - usual cost is somewhere between a few hundred pounds and a couple of thousand, depending on how thorough it is. Generally the more thorough surveys are appropriate for older houses. You might also want specialist reports on things like the electric wiring and the plumbing.
You need a solicitor or licensed conveyancer to handle the legal aspects, and there are also a few fees associated with those legal aspects. Typical total cost is £500 - £1000.
There might be a fee associated with getting a mortgage, but it depends entirely on the deal you get and should generally just be considered as part of the costs of the loan rather than the house purchase itself.