Do you need a billing system and a billing printer for your restaurant?
The answer is "YES" - any restaurant (however small) will need to give its customers a printed bill. A manual bill looks ugly, is prone to errors and misuse and you pretty much can't track anything. So you would atleast need to buy a bill printer, if not an entire billing system which you can connect to a bill printer.
You have fancy "Restaurant Software" with tools for billing, inventory management, Order management etc. (A google search will give your some results). You will need a standard computer to run these applications. The software if used well, can give you extensive reports for analysis e.g. Revenue by item, Revenue by time of day etc. From an investment perspective, such software will cost you between 15K to 50K atleast with an annual maintenance contract of 15-20% of the license value. In addition you will need to invest in a computer with a genuine Operating system (totally about 20-30K) and a bill printer for printing out the bills (about 4-10K). You will need to buy a POS (Point of Sale) printer (Wipro Peripherals, TVS Electronics & Epson offer quite a few options at various price points)
For starters, I highly recommend the standalone Wipro Retail Billing Units and NO - I don't have any relationship or commission arrangements with Wipro for this. In my opinion, they just have a great & unique product suited for practical Indian needs - especially for small retail units. Their system does the job well, is inexpensive (around 8-10K) to buy and run (cheap cartridges and printing paper rolls), does not need a computer or any software, provides basic reports for analysis.
Once your operations are stabilized, you can evaluate and buy a good system patiently. If your overall project is large, then evaluating and buying a suitable system upfront will be required.