Hi Benja
I see from your profile you’re a marathon runner so you should have no trouble with the stamina, I guess the key to what you need and spec wise is how competitive and serious you are re competing at Tri. The initial outlay can vary quite a bit depending on this.
If you just want to see what its like id go for a cheap bike (you can always relegate it to a training bike and get a better one later). As Sparks pointed out there are reasonably priced new bikes about. I would suggest you get a new one rather than second hand, also go to a good bike shop because the fitting is the key, e.g. correct alignment and distance between the pedals/handlebars.
On the other higher spec bikes (Giant, Cannondale, Specialised, Airbourne etc) start from £400 - £500 and the component specs, weight etc changes accordingly.
Along with the bike your going to need about £100 - £300 of other cycling kit – shoes, helmet, gloves, shorts, top, lights?, spare tube, pike tool, pump, tri bars?, bottle & cage etc.
You probably don’t need to worry about a wet suit for the time being as a lot of Tri’s have pool swims and you can also hire them otherwise.
Good luck.