If possible, it’s best to run with a monitor that has a chest strap; technology has come a crazy long way over the past few years, and wrist-based monitoring is definitely getting there, but a chest-strap is most reliable right now.
As for exact model, my advice is to go for the low-hanging fruit. Translation: You might not need to run out and buy a super-expensive and fancy new watch.
Did your current watch come with a strap that is sitting forgotten and unloved in a drawer? Grab it.
Is your current watch heart-rate enabled but you didn’t buy the strap at the time because you didn’t think you needed it? Get the strap that goes with your watch.
If you’re ready to upgrade your whole system, check out the price of the watch you want. Sometimes the stand-alone strap is pricey enough that it makes more sense to go ahead and upgrade.
Don’t have a watch because you run with an iPhone? Look at the available GPS apps like Strava, MapMyRun and Runkeeper. All will sync with different heart rate straps, so check prices and pick the combo that works with your budget.
Also bear in mind, I wear XL seamless training bras from the juniors section at Nike. Adding the heart rate strap to my chest is NBD. Many of my ‘gifted’ clients need to double-bag their chest and, as such, prefer wrist-based monitors. The only real downside to these is that you have to wear them really, really tightly against your wrist to get good, continuous heart rate data. If you have tiny wrists go for the chest straps, unless you are ‘gifted’ and a chest strap just won’t work.