It really comes down to personal choice cupajoe and the types of coffees you prefer to drink (short blacks, lattes, long black, etc.)
Irrespective of the coffee making technique, the key to a good cup is using freshly roasted & freshly grond beans of a good quality.
If you do not already own one your first purchase should be a grinder. The Rancilio Rocky is highly recommended and costs under $500. This unit should last you many years and would match up well to any of the methods you mention.
If you tend to drink long black coffees you could spend just $50 on an Aeropress. These are great little units that make a coffee quickly and are very easy to clean.
If you prefer short coffees or milk-based drinks then youre probably best off getting an espresso machine. In the price range you mention most would probably recommend the Rancilio Rocky & Silvia combination. Around $1300 for both.