Luggage and bags:
I suggest a good handbag for women, that can conceal your camera etc. I have had no problem with stealing. I always try to dress less like a tourist and with not too much jewellery etc. I have had no problem with stealing, however there are a lot of people begging in the streets, and I for some reason get targeted by the same person each time. So trying not to stand out makes sense. For me it is very confronting as I am not used to it and want to give them something but know I shouldn't.
Clothing/Shoes/Weather Gear: Definitely have an umbrella or rain jacket handy! It can be sunny one minute and rainy the next. Good walking shoes are a must if you plan to explore - most areas are cobbled or bricked so heels can be difficult.
Photo Equipment: A camera is essential - the churches and old buildings are great to take pictures of, the square as well. Also the less obvious areas make good pictures - the rundown buildings etc are a point of interest as they are so different to home.
Clothing/Shoes/Weather Gear: When you want to go there in winter you must pack all your warm clothes, there is always the same weather as in Bratislava but a bit colder. Last winter was pretty cold weather and some temperatures reached almost 20 degrees minus ;) brrrr