Hi Martin,
First, welcome to TBN.
You have almost exactly the same situation I do, including the terrain and weed species. I'm in the foothills and have 10 acres as well - got about 6 acres or so of exactly the same kind of growth you have there.
I have to mow mine two or three times a year. I consider it to be *mandatory*. The lovely green grass you see now will turn into a 6' tall mass of dead brush, which will burn so fast it'll make your head swim. There was one year that I was working a *lot* and didn't get to mowing - it was so bad I had a crew come in and do it for me.
A couple of people have already suggested it, but let me tell you... You need to get a tractor. There are services that will come in and do the cleanup for you (as mentioned), but they are expensive. It cost me $1500 the year that I let the pasture go to have it done for me (I do it in stages, chipping away at all that has to be done - they came in and did it in 8 hours).
You really do need to mow it, or at least put in firebreaks. Either one will have to be repeated every year. Renting a tractor capable of doing the work will cost probably $200 - $300 / day. In my mind this justifies the cost of a tractor - I paid $12000 for mine six years ago and the tractor still works great - and I don't pay for it any more ('cept that expensive diesel /forums/images/graemlins/crazy.gif).
Bird's advice on sizing is pretty good. That is what I wish I had bought. But what I have is quite adequate for my needs - a Kubota
B7300, 48" brush hog (and some other stuff that doesn't pertain to this thread). Going bigger would be nice - a 60" deck would sure be sweet. But if you're on a budget, sticking with a 15 - 20 HP tractor can save some cash.
Anyway, if you possibly can afford it, my advice is to go for it sooner, rather than later. Put the rental money (or what you'd spend to hire someone) towards the purchase now. That way you can save yourself a lot of grief by using it to help with your one-time work as well.
Let us know what you decide to do...