There are generally two solutions to layout problems:
switch to using grid. It becomes real easy to do layouts like what you are trying to accomplish. Grid can solve probably 95% of all layout issues (it's amazing when you think about it -- Tk does with one manager what most toolkits need half a dozen to accomplish!)
use multiple frames. If some widgets need to be stacked top-to-bottom and some left-to-right you can't always get what you want packing everything in a single frame. Use one frame for the top-to-bottom parts of the layout and additional frames for the left-to-right content.
Also realize that widgets don't have to be children of the widget in which they are packed/gridded. You can use the "in" parameter to put widgets in some other container than their parent.
For example, in your specific example you can create three frames, top, middle, bottom. Pack these top-to-bottom in your toplevel window. Then you can pack the first text widget in the top, the button or buttons horizontally in the middle, and the other text widget in the bottom.
The advantage to such an approach is that it makes it much easier to change the layout in the future (which in my experience always happens at some point). You don't have to re-parent any of your widgets, just pack/place/grid them in some other container.
In your short example it doesn't make much difference, but for complex apps this strategy can be a life saver.
My best advice is this: layout isn't an afterthought. Do a little planning, maybe even spend five minutes drawing on some graph paper. First decide on the major regions of your app and use a frame or some other container for each (paned window, notebook, etc). Once you have those, do the same divide-and-conquer approach for each section. This lets you use different types of layout for different sections of your app. Toolbars get horizontal layout, forms might get vertical layout, etc.