Yes!  It is your choice whether you hire or buy.  I would usually suggest you hire a saxophone for a few months to ensure it really is for you before going to the expense of buying your own instrument.

I recommend John Packer's own student model.  This is a relatively inexpensive way of getting started.  Currently (last checked 14/02/19) they charge £16/month and will send you out a brand new instrument by courier to get you started.  I also recommend you buy a Yamaha 4C mouthpiece which costs £30.  It will be easier to blow and help you create a richer tone. For more information follow this link to their website.
 

I would recommend you look around and do your own research into what instrument is best for you.  Again a good starting point would be John Packers in Taunton.  They have a huge range of saxophones in the different categories; beginners, intermediate and professional.  They have dedicated practice rooms where you can go and try out the different saxophones and get a true feel for what suits you. 
 
It also pays to ask around amongst friends, chat with me and look on the internet for reviews and individual player comments on the individual make/model you're interested in.
 
Prices vary, you can start with £349 for a basic John Packer student model, through to £3,000 upwards so it's important you do your research first before deciding which one to go for.