8085 is almost 34 years old microprocessor! I doubt if you will even find the 8085 chip in market.
I would suggest you to start with some microprocessor or microcontroller which is used in industry right now. Knowing new device will also help if you plan to take a job in embedded field. Go for 8051 family of microcontrollers. Its pretty old architecture but still very widely used in industry. Some of its very easy to learn/use variants are AT89S51/AT89S52, P89V51RD2, P89C61X2, AT89C2051 etc.
All these variants have inbuilt flash ROM, so you don't have to connect any external latch or EPROM like with 8085. Plus there are tons of tools, resources and hardware available online to get you started.