What's the ideal way to see if a database is available on the SQL Server using TSQL? It appears multiple methods to implement this.

From the Microsoft's script:

DECLARE @dbname nvarchar(128)

SET @dbname = N'Senna'

IF (EXISTS (SELECT name FROM master.dbo.sysdatabases WHERE ('[' + name + ']' = @dbname OR name = @dbname)))

  -- code mine :)

  PRINT 'db exists'

Really it's more optimal to make use of:

if db_id('dms') is not null
   --code mine :)
   print 'db exists'
USE [master]

IF EXISTS (SELECT name FROM sys.databases WHERE name = N'YourDatabaseName')
  Do your thing...

Incidentally, this came from SQL Server Studio, therefore if you can get it, I suggest you start having fun with the different "Script xxxx AS" functions that are offered. Can make your existence simpler! :)