Dont go lifting any lids anywhere, your too new to the scene to know what you're doing or to do it safely and leave them safe afterwards.
Its not a case of the round ones are for people and the triangle ones are for cats its a case of you'll kill yourself or someone else if you get it wrong.
Some of these covers haven't moved for a long time and especially the cast iron ones you've a good chance of breaking them or your back. Then I assume you'll leave a hole in the street.
Putting a cover back without seating it properly is a good way to have a car smash through it or someone trip over it or as said have it coming crashing down on your head.
Being found with lid keys is going equipped and also keys are for specific covers no doubt you'll end up trying to prise lids up with what you have because they don't fit properly.
Its not like that fat twat ewf where you walk up to a lid and travel down into underground Manchester (that one is now sealed i beleive) he was relying on others wanting their 5 minutes of fame.
You don't walk round and see a certain type of cover and say those cover secret tunnels lets go down it, all types, shapes and makes of cover are used for anything. You need to research what you want to find, where you want to go, which lid might see you to where you need to go and then look for a lid that may achieve that and only then look at the lid properly and im sorry to say you just don't have any of those skills at the moment.
You're talking about moving lids clear of their holes before decent and what? Leave an open hole while your having your jollys underneath? You won't even be able to move a lot of lids clear of any hole without a lift and rollers anyway.
Take some advice, sell your keys or hide them in your shed for a couple years, you really aren't experienced enough, the fact you're asking which type of lid leads to underground tunnels shows you've no idea. Seriously stop now before you hurt someone.