While it would be preferable, as Andrew suggests, to use styles for the body and bullet paragraphs, your macro will do what you require if you add code to reset the paragraph format and font of the pasted text.
Note also that as this works with paragraphs, you will get some odd results if you paste text that has line breaks rather than paragraph breaks e.g. pasting from your message example.
Code:
Sub BulletsAndSizer()
Dim aRng As Range
Set aRng = Selection.Range
aRng.Text = Replace(aRng.Text, Chr(11), Chr(13))
If Len(aRng.Text) > 0 Then aRng.Style = "List Bullet"
With aRng
.Expand Unit:=wdStory
.Font.Reset
.ParagraphFormat.Reset
.Font.Size = 18
.Font.Name = "Times New Roman"
End With
Set aRng = Nothing
End Sub