If you want the cheapest solution, then you want to get a HR Belt that will work with your iPhone. This means it will need to be bluetooth, and Polar make the H7 bluetooth belt for about £50.
A dedicated GPS watch with HR belt is a popular option, such as the Garmin Forerunner range. You should be able to get a forerunner 110 with HR belt for £115 from amazon (maybe cheaper else where). The HR belt with the Garmin uses the ANT+ technology to connect to the garmin watch, so this belt won't connect to your iPhone.
With the garmin, you can download the data from the watch onto your computer, and then synch this with web-based training programs.
See link below to the basics about running and HR training, there are more details on this site (and others). You don't want to use the 220 - age to calculate your Max HR, you need to do a test to calculate your personal Max HR.
To kinda answer your question, as a guide I'd expect to be somewhere between 90 to 95 % max HR during a 10k, whereas I might go above 95% in a 5k (and would try to stay under 90% at all times for anything further than 10k)
If I'm reading this correctly, its the same thing we all "suffer" from when we run faster. The technical terms are anaerobic threshold and reaching VO2 Max (if you want to google them).
The basics are, as you run faster your muscles need to work harder. Harder working muscles use more energy, and they also need oxygen to help consume the fuel that creates energy. Every person has a limit of the amount of oxygen they can inhale (i.e. your VO2 max) at a given time, but we all have different limits. Your muscles are asking for more oxygen than your body can provide, hence the heavy breathing to try and get as much air as possible.
The good news is that you can improve this, with longer, slower runs making your running more efficient (so not as much fuel required for a given pace). You can also improve your VO2 Max by stressing your breathing system through repeating short, fast runs that push your body and make it adapt to increase your oxygen intake (i.e. interval sessions like 6x 400m at 5k pace or higher etc).
Hi Amanda, is the knee heavily bruised? I had a knee arthroscopy last year, after five weeks it was still very stiff and was a beatiful shade of yellow. This surprised me as the healing time was to recover from the bruising caused by the surgical tools, rather than the trimming of the meniscus. Have you seen a steady improvement in knee movement? Has the swelling been gradually reducing? These might not be at the rather that you'd like, but it should be getting noticeably better as the weeks progress.
My experience was that I wasn't given any physio (nor crutches). I was seen privately - so there was no ulterior motive to save money. I'd targetted eight weeks post-op to start running again, but this was optimistic and it turned out to be 12 weeks before I could run. I do remember my recovery being frustratingly slow.
Whilst I didn't have any physio, I did follow my own routine based on advice I'd found on the internet (a fairly conservative approach as I ignored a lot of the more extreme internet "advice"). This mainly consisted of gentle bending and tensing of the thigh muscles etc, as there was no way I was capable of doing squats etc.
Have a look here for some advice from an NHS Trust (NB note that they mention follow up physio is not normally provided for a menicus tear).