Hey! Funnily enough I was looking into this myself this morning! I have a fitbit blaze and I also have an old oregon science watch with a strap monitor which is pretty damn accurate. The blaze is only really accurate for heartrate at rest. I've worn both when I've went into VT and my blaze tells me heart rate is 150 whereas my oregon watch says 236.
Overall, wrist monitors by themselves are less accurate than chest monitors. Chest monitors can often be used with a watch and/or a phone. Personally, I'm thinking of getting a chest strap that links to my phone and save the money on a new watch, but that's only because I already have two heartrate watches. I just want a strap that I can store my heartrate and monitor over time, whereas my oregon one just shows my heartrate there and then and doesn't store it. Anyhoo... I recommend you go for a wrist monitor that can be used with a strap, rather than e.g. a fitbit which isn't massively accurate and can't be paired with a chest strap.
So, this morning when I was googling it, for wrist monitors, the one that got the thumbs up on a wearable forum was the Polar M430 and the tomtom spark 3.
The best chest straps that link with phones etc includes the Polar H10 (or the older H7), or the Wahoo Tickr X.
There's also a new kid on the block, the Wahoo Tickr Fit, which is worn at the top of the forearm. Apparently it can produce results on par with a chest strap.
I think I'm going to go for the Polar H10. Hope this has been helpful in some way! Would also like to hear from people who actually have experience in a good one so will be following this post :)