Does anyone use a device that combines all of these functions? There are a lot on the market and I'm not sure which one to choose.
I use a Garmin 305 when running. They don't make those anymore (the 310xt and some other one have "replaced" the 305). I got my girlfriend a Garmin 110 and she really enjoys it. The 210 is another viable option but cost a little more. I'm partial to Garmin (clearly ;) but Timex and Polar make pretty good HR monitors as well.
The price point for getting one to include pace (either GPS enabled like the Garmins, or perhaps foot pod enabled like some of the polar models) is probably $175ish, but if you look around you can find them for less (the 110 with HR strap retails for $229 on the Garmin Website but I bought it online via Amazon for $170).
I'm sure those who chime in here will all have different opinions--it's kind of like the type of car you drive, the type of pump or shot therapy you use, etc. Everyone has their preference.
Read some reviews online after you get some suggestions here, go with what you like, and I'm sure you'll be good to go :)
I've used a couple HRMs, but currently have been using the Wahoo Fitness HRM (works with an iPhone) which covers some additional elements and can be uploaded to Training Peaks, Strava, etc.
I have a Garmin 405, I think the new model is a 410. I like the size of it as I've seen the slightly older models that were clunkier. It is very versatile and has all sorts of options for displaying the data on up to 3 screens of 3x numbers each, which you can tailor however you want speed/ dist/ time, elevation/ pace/ lap speed, HR, AVG pace, etc. There's a "ghost" screen so you can race yourself or pace yourself according to prior runs. I don't use all of the capabilities and have slacked off on the HR meter but, when I used in the past, it worked very well.
The only problem I had was that at the Chicago Marathon, you run under this bridge that fried it out so I ran too fast last year. It recovered down the road but, by then, I had been at it for a while and ran out of gas. More my fault than the Garmin's but it threw me off a bit.