Remember you will need about £3-4000 to cover legal, administrative and removals costs involved in purchasing. Still, you should be able to put down a 20% deposit on the house (£17,200) and allow the rest of the money for costs.
Because you are only on a temporary contract you may not be considered a 'safe bet' for a mortgage. However if you are only taking out a mortgage of £68,800 (the remaining 80% of the purchase price after a 20% deposit) then I would have thought your partners permanent earnings alone would be enough to get a mortgage with, unless he is on a very low salary. Your mortgage broker should be able to advise though.
I would also always advise spending a few hundred on getting a proper survey done on somewhere before you buy it, so you know if there any big repair bills in the pipeline.
Do always view somewhere in person. Estate agent pictures can be deceptive.
If you decide you like it, it's worth considering if you can get the money off the asking price. Although this depends on how realistic the asking price is for the area, how long the house has been on the market for, and how keen the owner is to sell.
After that phone a few solicitors and get some quotes. One you have chosen your preferred solicitor just phone them and tell them you want to instruct them to do the conveyancing for you, and they should then send all the necessary initial paperwork out to you.
The one piece of advice I wish I'd been given as a FTB is chase everyone (solicitors, mortgage companies etc), and follow up that things have been done on time! Communication in this process is often not great in my experience, and you often have to chase things up yourself to find out if there are any issues / why the process has stalled.