Welcome to CoffeeSnobs.... [smiley=thumbsup.gif]
If I was in your position mate and more or less just starting out with a limited budget, Id be upgrading the Grinder to the best "real" burr grinder that you can afford and then brew with an AeroPress or something similar. The Braun just doesnt cut it for decent espresso Im afraid.
If you do a bit more research though our Forum and other reputable forums like Home Barista or Coffee Geek you will find stated time and time again... The Grinder is way the most important piece of coffee hardware you can own, the brewing method is nowhere near as important. If you always ensure that you are using freshly roasted, high quality beans from a reputable specialist roaster and only grind enough coffee immediately before brewing, you will discover the wonders of great coffee and then realise why we are all so passionate about it here at CS.
Once you have a decent grinder, you can always save up for a more competent espresso machine for purchase later on but you will always find that something like the AeroPress will always come in handy, even if it is to make just one coffee and you cant be bothered turning the espresso machine on. It will never become redundant.
Pretty well all of our Site Sponsors sell good grinders, from entry level machines all the way up to professional competition beasties. CuppaCoffee also happen to sell the AeroPress and Dennis (the proprietor) will look after you the same as if you were buying a $5000 top of the range combo. Well worth taking the time to discuss your requirements with the budget you have at your disposal. Links to all of our sponsors are listed over on the L/H side of the page.... <----- Over there ;)
All the best mate and happy brewing... :)