Can I get the # of :GetChildren but only with children that meet a selected criteria?

It is not possible with just :GetChildren, however you can make your own table.

function GetChildrenWithName(object, name)
    local ChildrenWithName = {}
    for i,v in pairs(object:GetChildren()) do
        if v.Name == name then
            table.insert(ChildrenWithName, v)
        end
    end
    return ChildrenWithName
end

local Amount = #GetChildrenWithName(workspace.Folder, "Part")

You can do this with :GetChildren() and a variable

local Count = 0
for i, v in ipairs(game.Workspace:GetChildren()) do
    if v:IsA("Folder") then
        Count = Count + 1
    end
end
print(Count)

Count should print the amount of children that meets your selected criteria