I'm just going to back up a bit. You're doing PPL training, and you're finally getting away from the circuit. That's great, but honestly you will not be doing x-countries of hundreds of miles just yet. In fact, you'll probably make less than 10 or so flights that will take you over 100 mile away from home base in the course of your PPL training. And once you get the PPL you'll want to expand your range slowly.
If you happen to be very unlucky and get that radio failure when you're far away, you can just land at the nearest uncontrolled airfield, phone the school what happened, let them sort it out and hire a car or something to be home for dinner anyway. In other words: It's not a necessity, but an extra, to have a handheld radio, given the type of operations you're going to be doing in the near future.
If you have budget to buy extras such as handheld radios, I would prioritize things differently. First, I would buy a good headset. Maybe one of those ANR ones, or an in-ear headset. Second on my list would be a good GPS, or (like I have) an iPad with a decent navigation app (SkyDemon is the best option in Europe, I don't know about Canada).
If you fly over hostile terrain a lot (which I can imagine in Canada) my third choice would probably be a PLB and possibly some other survival kit. And in very busy airspace, a PCAS such as the Zaon MRX/XRX or PowerFlarm. A handheld radio would probably come in fourth or fifth place on my list of priorities.
If your main worry is a comms failure, then your priorities may be different of course. If so, the Icom seems to be the most popular, and I can only endorse the tips others gave (headset adapter, 8.33 kHz spacing, some sort of hookup to an external antenna, and maybe a means of hooking it up to the aircraft electric system as well). Don't worry about them possibly being illegal - nobody is going to question you about that if you just had a for-real comms failure.
But another alternative would be to get one of those mobile phone-headset adapters, which allows you to use your mobile phone with your headset. Some ANR headsets even have such an adapter built-in. A lot cheaper than an Icom, smaller so easier to stow in your flight bag, and doesn't need batteries.