I recommend Clover. Clover is a combination of hardware (PoS terminals, printers, barcode scanners, etc.) and software.
Starting with the hardware, you have three options.
Each of these can take user credit cards. The Station is your main cashier terminal. It is stationary. The Mini is an "extender" for the Station. These are useful for surges - ie. the yearly festival in your town that causes your business to have lines around the corner for a weekend. They provide much of the functionality of the Station, but you don't need it much of the time. The Mobile is useful for the traveling server. They can carry it to the table and place orders, or during your hypothetical yearly festival, can travel down the line of customers and take their order before they get to the Station.
Along with the base PoS stations, Clover has several accessories. These include barcode scanners, printers (including kitchen printers), weight scales, debit pads (though, the same functionality is available on the PoS terminals themselves) and more.
Next comes the software. Clover has an App Market with a large amount of add on applications. The downside is that many of these are monthly subscription based. I encourage you to look through these apps though. I can see several that look like they'd be useful for a diner (including tip suggestions). There are also things that aren't Point of Sale specific. I see apps for time clocks, inventory management, multi-store management, coupons, analytics of your customers and more.
Lastly, there is a developer API (which the apps in the App Market use). If you find there isn't an app that you need and you have developer experience (or can hire a developer), it appears that there is code and documentation available to help you do it.
Regarding your question about credit cards, Clover provides you with a Merchant account on First Data. If you have a merchant account with someone else, Clover encouages you to talk with them to see if they sell Clover.