About as simple as it can get, yet functional. Able to open long filenames and the filenames can contain Unicode charaters (of course you need to use file API to obtain such filenames).

Code:
'clsMCI.cls
Option Explicit

Public Event Error(ByVal Message As String)

Private Declare Function mciGetErrorStringW Lib "winmm" (ByVal dwError As Long, ByVal lpstrBuffer As Long, ByVal uLength As Long) As Long
Private Declare Function mciSendStringW Lib "winmm" (ByVal lpstrCommand As Long, Optional ByVal lpstrReturnString As Long, Optional ByVal uReturnLength As Long, Optional ByVal hwndCallback As Long) As Long

Private m_Error As String
Private m_ID As String

Private Sub MCI(Command As String, Optional Success As Boolean, Optional ByVal IgnoreError As Boolean)
    Dim lngError As Long
    lngError = mciSendStringW(StrPtr(Command & " " & m_ID))
    If lngError Then
        If Not IgnoreError Then
            m_Error = Space$(260)
            mciGetErrorStringW lngError, StrPtr(m_Error), 260
            lngError = InStr(m_Error, vbNullChar)
            If lngError Then m_Error = Left$(m_Error, lngError - 1)
            RaiseEvent Error(m_Error)
        End If
    Else
        Success = True
    End If
End Sub

Public Function Continue() As Boolean
    MCI "resume", Continue
End Function

Public Function Halt() As Boolean
    MCI "stop", Halt
End Function

Public Function LastError() As String
    LastError = m_Error
End Function

Public Function Load(Filename As String) As Boolean
    MCI "close", , True
    MCI "open """ & Filename & """ alias", Load
End Function

Public Function Pause() As Boolean
    MCI "pause", Pause
End Function

Public Function Play() As Boolean
    MCI "play", Play
End Function

Private Sub Class_Initialize()
    m_ID = "mp3_" & Hex$(Timer * 1000)
End Sub

Private Sub Class_Terminate()
    MCI "close", , True
End Sub
The following sample will open two files and plays both the same time. If there are errors, debug console will get messages for the first one.
Code:
' Form1.frm
Option Explicit

Private WithEvents MP3 As clsMCI
Private MP3b As clsMCI

Private Sub Form_Load()
    Set MP3 = New clsMCI
    If MP3.Load("C:\Users\YOU\Music\Test.mp3") Then MP3.Play
    
    Set MP3b = New clsMCI
    If MP3b.Load("C:\Users\YOU\Music\Test2.mp3") Then MP3b.Play
End Sub

Private Sub MP3_Error(ByVal Message As String)
    Debug.Print Message
End Sub
FYI: Multimedia Command Strings