Integrated brake shifter levers are, in my opinion, totally awesome, but it'd be financially silly to upgrade your bike to them, as they're rather expensive in the first place and would require an almost complete drivetrain upgrade. The way to get this style drivetrain is really to buy a bike that comes stock with them, unless you want a high end steel frame, in which case upgrading makes some sense.

You can probably learn to shift OK with downtubes. Practice makes perfect.

Most people (myself included) like bar ends a lot better than downtubes, and if you're already riding in the drops a lot they're really convenient. Spending up to $60 is probably a semi-reasonable decision, and it's a relatively easy upgrade. You'll also probably need new shift housing and cable. Don't worry about what they index to, just get whatever you can get cheap. Shimano bar ends can be set to friction to use most any drivetrain, and the cheapest commonly available are their 8 speed ultegra, or you can probably find used Suntour shifters.