Some people think that roleplaying is an expensive hobby, and it can be. But with the right kind of innovation it can be almost completely costless!
I myself have little money these days as a poor college student but that does not keep me from roleplaying. I will tell you what kinds of things people use for roleplaying and cheaper replacements of these items.
When I first started DMing I had absolutely nothing. When my group went into battle we kind of just imagined it. This was my sloppiest times for DMing. Sometimes in battle I would lose or gain monsters due to the lack of way to keep track. The monsters stats were often made up in my head and inconsistent between the same monsters. After a while I started using paper to just briefly mark down where things were at and the stats but it still gave the players a headache to try to remember where everything was at.
This is why a board is one of the most important items in Roleplaying with elaborate battle systems. Boards can be bought and range up from 5$ to 30$ mattering on the size, ability to draw on it, and other factors. The first kind of board I used was a large poster board that I had measured out and drawn a grid on with sharpies. This was great and worked perfectly well. The only issue is I could not indicate other objects on the map.
For the monsters I used erasers and I Heroclix figures used for the players. After a while I decided that the battles could become more interesting and elaborate it I could somehow dictate setting. Many people use little models that are sold online or at conventions. These look really nice and professional but can be extremely expensive over time. So instead I bought a dry erase board and once again drew a gird on it with sharpies. I than was able to draw in floor plans and sky view of the setting with dry erase marker and it was easy to change between battles.
Some of my players got really ambitious after we played for a while and bought their own miniatures. This was awesome because now we had figures that actually looked like the characters instead of, for example, a tiny figure of a robot to represent the Halfling paladin. These are not a necessity and it is not the entirely the DMs duty to provide them. Over the time, as a player, I collected my own miniatures and make them available to the players as characters.
Anyone can do the same for monsters and by miniatures and figures to represent the monsters. This requires many unfortunately if you want them to be an accurate description of your monsters. For a while the only monster figures I had been kobolds so for a whole month my party only battled kobolds. They became incredibly tired of this.
The one thing that I can say with certain you will need without a doubt is dice. Dice are not too expensive. Most people like to buy them in sets which on the internet and at conventions can be 3$-12$. You can even look more official if you buy a dice bag to hold these dice in, but this is not a necessity. I have never owned my own set of dice but instead of opted for the large bins of miscellaneous dice at conventions that you can buy a pitcher full for only 15$.
At least one person in the group has to have one of each type of dice including d4, d6, d8, d10, d12, d20. This is the absolute minimum but I highly suggest one of these sets for each person. I have played this way before and it becomes incredibly vexing when you have to pass one d20 around every time people have to make a perception check. Avoid this at all costs!
There are other small objects that can come in handy. Having a monsters manual or general rule book of the system you are playing is helpful and can make keepings stats for monsters easier. Instead of grid boards I have seen tile pieces that create elaborate flooring and this can spiffy up the battle. I had a player once go and buy an entire set of these tiles (which are quite expensive) and now whenever we have sewer battles we use the tiles and it looks amazing.
Overall this can seem quite expensive. Sometimes this can keep people from beginning roleplaying. If you are committed and on a budget all you absolutely need is a fine group of players, a good set of dice, character sheets, and a desire to role-play. Because outside of battle players are the only thing you need to make the game run smoothly.