Is your Tiagra crank a compact (a double) or is it a triple? What range of gears will you be running? That can affect the cage length needed on the rear derailleur. Your setup guy should be able to advise you on that.
You can use Tiagra or the older 10 speed 105 or even the older 10 speed Ultegra derailleurs (current 105 and Ultra are now 11speed), but cost goes up in a hurry. However, you might find a closeout on the older 10 speed versions of 105 or Ultra, so shop around. Unless you really plan to pile on the miles, though, Tiagra will do fine for your derailleurs and it is quite affordable.
On the handlebars, check to make sure you get the proper width. For some of us gals, the standard widths are a bit too wide.