I think this would depend on the usage. If you are frequently needing to access the 'Second' or 'Third' items without the containing 'First', then perhaps they are better not being embedded.
A question I have used to help me determine whether something might be better embedded or not is to ask myself whether it is part of it or related to it. E.g, does a 'First' actually contain one or more 'Seconds' (and so on), or are they separate things which happen to be related in some way? On the face of it, I'd say a blog post contains comments (unless you have a compelling need to query the list of comments without knowledge of the posts), but a user/*author* probably does not contain a list of posts, rather they'd be linked in some way but reside in different collections.
Cross-collection relationships can be achieved with MongoDB using DBRef. This is a special type which describes a relationship with another object. If your items do belong in their own collections, they can have a DBRef to point between each other. These could go whichever way round you want (i.e. a collection of them in the First, or each Second could have one pointing to its parent first).
Example 1 - each parent has a collection of child references:
db.firsts.findOne()
{
"_id" : ObjectId("..."),
"Seconds" : [
{ $ref : 'seconds', $id : <idvalue> },
{ $ref : 'seconds', $id : <idvalue> },
{ $ref : 'seconds', $id : <idvalue> }
]
}
db.seconds.findOne()
{
"_id" : ObjectId("..."),
"Second Name" : "value",
"Thirds" : [
{ $ref : 'thirds', $id : <idvalue> },
{ $ref : 'thirds', $id : <idvalue> }
]
}
db.thirds.findOne()
{
"_id" : ObjectId("..."),
"Third Name" : "value"
}
Example 2 - each child has a reference to its parent
db.firsts.findOne()
{
"_id" : ObjectId("...")
}
db.seconds.findOne()
{
"_id" : ObjectId("..."),
"First" : { $ref : 'firsts', $id : <idvalue> }
"Second Name" : "value",
}
db.thirds.findOne()
{
"_id" : ObjectId("..."),
"Second" : { $ref : 'seconds', $id : <idvalue> }
"Third Name" : "value"
}
Most of the MongoDB language drivers has a way of dealing with dbrefs in a neater way than on the console (normally using some kind of 'DBRef' class). Working this way will mean you have more database requests, but if it makes sense to your application, it's probably a fair compromise to make - particularly if the list of 'Seconds' or 'Thirds' in your example are commonly needed or key to interaction with the system or its functionality.
The second approach is most like you would have using a traditional relational DB. The beauty of MongoDB is that it allows you to work relationally when it actually makes sense to do so, and not when it does not. Very flexible, and ultimately it depends on your data and application as to what makes sense for you. Ultimately the answer to your question of which method you should use depends on your application and the data it stores - not something we can tell from your example.