We have tried eggs in the beginning to save time but if one of them breaks, then its a mess, boiling milk is OK as long as you stay close to it. But cleaning both leaves a smell that we don't like so we have stopped it.
We have tried a few brands, most of them get spoilt after a year ( may be because of the water we get), many come with lids that are attached and are off non-metal make. Currently, we have been using Prestige 1.7 litres, model PKGSS 1.7 lts for the last 1 1/2 years without any issues. This has a wide rim with the same dimension from the top to the bottom. It has a tempered glass lid with a vent that we find it useful because kids and we many times have switched on then found that the water is less in it. This is excellent for washing, hands go in easily. The only drawback is that it does not have any markings and we use it for water and noodles, but NOT used for milk. This is an indispensable item for us in the mornings. The price is around 1200 rupees,
The Prestige 41574 is one that can be used for water and cooking purposes. You can check this out.