The days of free shooting are long gone, if you are still lucky enough to have some hang on to it it won't last
Regarding deer being a pest depends on the species some of the bigger species will certainly damage crops, Roe do practically no damage to crops , woodland is a different matter, however this can work in your favour as many farmers seeing Roe on a field of young grain think they are eating it when they are in fact picking out the emerging weeds, Roe are browsers not grazers and as such don't eat a lot of any one thing.
In any case deer are only a pest if the landowner sees them as such, in many cases the landowner will see deer as crop that can provides a financial return, especially if the lease holder can be depended upon to keep any potential
damage to a minimum, try to reach a mutually agreeable price for the ground,(everybody wants a bargain but don't try being a cheap skate have a look at what leases in your area are making as there is a bit of variation across the country,get it in writing and if you are paying for a lease you want exclusive rights, expect to increase your rent by around 2% per annum, try to get a five year lease on the ground rather than yearly ( but payed annually of course)
By doing all of the above the landowner will see that you are serious , the five year lease at least and the annual increase of payment though small goes someway to preventing the fly by night who might try to approach the landowner with the intention of taking your ground.
As the previous poster said try to come to an arrangement where you are paying by what you can realistically take off the ground rather than by the acreage though many private lets are by the acre.