I want a heart rate monitor for working out and cycling. The strapless ones sound nice, but I have never used any heart rate monitor so I don't know.

Strapless:
E Pulse 2 - https://www.amazon.com/ePulse2-Strapl.../dp/B003YDOO2K
Mio Drive - https://www.amazon.com/Mio-Drive-Spec...dp/B0031YGNYE/

Strap:
Suunto M1 - https://www.amazon.com/Suunto-Heart-M...dp/B003VQ4VIW/

Other suggestions?

Almost all strapless hrms do not take continuous heart rate, and require you to touch a button with your finger to get a reading. Some new stuff is coming to market that will change this but it's an emerging technology. However, it looks like the epulse 2 is continuous? It has horrible reviews though.

I recommend getting a hrm designed to work as a cyclocomputer. Some of these will also work with a wrist strap off the bike. You really want hrm info to be easy to read to be useful on the bike.

I have a wireless Sigma I've been happy with. The chest strap doesn't really annoy me.

I've used the strap type for years, riding, running, at the gym etc.. Once I get going I'm not even aware of it.

if you want continuous readings a chest strap is required.
i have been using timex hrm with strap like this one, https://www.ebay.com/itm/Timex-Ironma...item5d38249133 for years without problems.
last year i upgraded to a cateye v3 bike computer. i like it a lot.
now the timex stays on my spin cycle.

I really want a wrist one because I do a lot more than just bike, especially in the winter. Why would I need something bike-integrated?

This Timex is rated pretty well, and only $70. One of the lower priced one has battery suck issues according to reviewers, so that concerns me a little.
https://www.amazon.com/Timex-Ironman-...dp/B001GWYACK/

the one you have in your link is digital. i have used the analog ones for years without problems.
yes the batteries go bad quickly in the chest strap. i usually replace mine every 2 months or so, batteries are usually less than $5 for 2 at walgreens.
people who have problems with the watch readings probably don't have moisture on the chest strap or have the chest strap on upside down, mine is that way.
as posted earlier the wrist ones you must touch your finger to a sensor to get readings. with a chest strap you get continuous readings updated every 10 seconds or so, don't ember the exact time.

been using one with straps since the mid 80's, once you get used to it, it not ever an issue.. the strapless ones are not very accurate.

Anyone have experience with the Polar RCX3? It has some cycling features, seems pretty nice. A little more than I was hoping, but maybe worth it.

https://www.polarusa.com/us-en/produc...ultisport/RCX3

How well do the chest strap HRMs work for people with a hairy chest? I always have problems getting an EKG and sometimes have to shave areas where the electrodes attach.

I have noticed they make electrode cream type stuff... maybe that would help?

Still trying to decide on a monitor... I'm now between getting a cheap Polar that will work with treadmills at the gym, and going all the way to a Garmin 310xt. The Garmin stuff looks pretty awesome, but $250 is a lot more than I had planned on spending.

i have a pretty harry chest. i really don't have a problem with the chest strap other than replacing the batteries often.
you need moisture to get them to work properly. i put a fair amount of saliva on the back side with my fingers when i start out and i sweat pretty good so it stays wet when i use it.

I went with the Garmin FR70.