I have a Blaser R93 and in my view they are good rifles. However, they are not to the taste of everyone and so you'd certainly need to have a play with one and see if it suited you. Also if you are operating on a tight budget and especially if you are just starting out then it would be worth considering that the money might be better spent on some days stalking - if you stuck to your budget of £1000 and had £1500 in the kitty then the £500 left over might pay to take you to Scotland for red hinds for a few days. Also I don't know what other gear you need but if you are looking at binos and slips and slings and cleaning gear the cost of that stuff isn't long in mounting up and the extra £500 will not go very far at all.
On the other hand if you are not intending to chop and change rifles, as some people do, then it is worth buying right in the first instance as you are going to have the rifle for a long time. I've had my Blaser for quite a few years now and have no intention of changing it and so am very glad that I bought a good rifle that is easy to travel with at the outset. The one thing with the Blaser is that it is not a "full time hobby" in the sense that you will not be changing triggers and bedding the stock and so on. The Blaser is just a simple tool that you use straight out of the box with no need to spend another few years getting it to shoot right.
I guess only you can balance this one up in your head but I'd say if you are viewing the rifle as a long term, once in a lifetime, purchase then it might be worth saving for longer and going for the best quality you can afford. However, if you are prone to changing things around a lot and especially if you are new to stalking then I'd seriously consider buying a relatively inexpensive but decent shooting rifle, Parker Hale comes to mind but isn't the only option, and spending the rest on stalking days - take yourself to Scotland and shoot red hinds over the winter as red deer on the hill in Scotland really is something everyone should do and once you go your only regret will be not doing it sooner.