In case you don't mind paying near to $250 on a fitness watch, you need to check out the Garmin Vívoactive 3. This is the best ever I could suggest within your budget and also it has all the features you want like you said above. BUT, if you need to make a second choice, you should consider the Fitbit Ionic.
It is like a straight fight between Pepsi vs Cola, DC vs Marvel, PS4 vs Xbox One, Android vs iOS. So the rival for Garmin is Fitbit. You can take a look at the comparison or read review before making final choice.
Some additional info.
Fitbit Ionic = 50 grams (or to be exact = 49.8952 grams)
Garmin Vivoactive 3 = 43 grams
So the winner here is Fitbit Ionic
Battery life :
Fitbit = 4 days
Garmin = 7 days
So the winner here is Garmin Vívoactive 3
Software Compatibility and Features :
Garmin - If you are really into fitness freak or maybe something like endurance athletes and detailed performance junkie. This is the best to utilize a lot of activities such as cycling, golf, skiing, sports tracking, etc.
Fitbit - It is preferable for people who desire a less complicated user interface, are keen on daily activity monitoring and get social functions.
What you stated above "track calories consumed, burnt and also help manage time allotments to various activities like sleep, eating, etc.."
It is all can be done via both fitness tracker, but in term more added function or more details tracking, the winner is Garmin is here. But if you are not really into that, the best is Fitbit Ionic, with great display quality (that is the thing that make the battery duration for the Ionic less than Vivoactive) and less complicated user interface, it could be great for you which is at home the most of the time.
Finally, my guess, the Fitbit Ionic is more suitable for you. For more details specs, i guess you should check out their official website, it might be a very long answer if i need to elaborate all of the details aspects and features.