In general, I caution against abandoning anything tried-and-true just to be current –some current things are fashion statements rather than usability advancements. If you’re really think it’s important to keep the commands “mostly out of the way until they are needed,” then use a menu bar. It looks like all you need is a File and Help menu, so it’ll constitute very little clutter indeed. Maybe you can even use the space after the Help menu for something other than commands (e.g., status annunciators), making your design more compact. Anything more current than File and Help is likely to be less familiar to your users, and therefore more likely to be confusing.
However, there is definitely an advantage to not hiding your commands like the traditional menu bar does. Displaying all the commands full time makes it easier for users to find commands and, by sheer exposure, more effectively educates the users on the capabilities of the app. When you have so few commands, and at least some of commands are used in every session, it makes more sense to display them in a single-level menu rather hide them in pull downs. Another issue with the menu bar is that it requires two clicks (or a click and drag) to select an item. In contrast, displaying the commands in a single level takes one click, making a more efficient design.
Perhaps you should put all the commands in a button bar. If you want, you can use split buttons where you want and put rarely needed commands (maybe Save As and About) on the drop-down. Such a button bar would take up no more space than a typical toolbar or multi-menu menu bar, so I wouldn’t worry too much about it being in the way.
Another option is to place the commands in a vertical bank of buttons on the left side of the window, web-style. Users can scan down a list of commands more easily that across.