A water cooler is probably the best bet for home use. Price wise they are reasonable, but depending on your transportation situation, acquiring those gallon jugs might not be the easiest thing for you to do.
For water filtration, there's obviously the table top ones, also the option of buying a bottle such as Brita and other brands that have a water filter built in. This way when you top up at a water fountain etc. on the go, that water is filtered too.
https://www.amazon.ca/Brita-Premium-...9803204&sr=8-5
https://www.amazon.ca/Brita-Premium-...9803389&sr=8-8
https://www.amazon.ca/LifeStraw-Bott...9803389&sr=8-6
It seems like the Brita ones need a $5 filter replacement ever 2 months.
https://www.amazon.ca/Brita-Water-Bo...6T4FEEQZNAWXB8
The life straw one is a $6 filter that is rated for 100 litres (3 litres a day = approx 1 month). But goes as far to say it can get rid of bacteria and parasites which the Brita one isn't rated for. I believe life straw started off trying to do potable water in the wilderness, so it's higher end than the Brita filter which is designed for use on tap water.
https://www.amazon.ca/LifeStraw-Carb...RWCPVK34WTYNQ8
That bottle filter doesn't reduce lead and other heavy metals though according to the comparison of life straw products below, but there's a home filtration option from life straw that can apparently reduce lead. I know you mentioned it in your post as a possible concern so I guess it's worth mentioning that not all filtration systems filter those heavy metals apparently.
https://www.amazon.ca/dp/B07QN17RVC/ref=dp_prsubs_1
Tap water filters like those Brita things aren't that great and gunk up quickly so I'm not sure if it's really that much more environmentally friendly (less space I suppose). Not to mention many people get lazy with them/install them incorrectly and are essentially not realizing they are no longer filtering their water because the filter is shot, but they don't realize this.
A higher end tap filtration system (ie: reverse osmosis) is much more expensive and some have non-stop gurgling noises. I wouldn't personally recommend them.