Text boxes are related to form design (a set of objects to enter data interactively). I don’t think this is what you want. Unless you know what you’re doing, stay away from text boxes, they live outside your text flow.
According your description, you’d like some border around text.
For the rest of this answer, I’ll assume you’re a newbie and don’t know anything about styles.
##Border around a paragraph
With the cursor inside the paragraph, Format>Paragraph and go to the Borders tab. Create your custom border with the available settings.
##Border around a sequence of words
Select the sequence of words, then Format>Character and go to the Borders tab. Same settings are available.
If you must repetitively apply these formatting, record them in a paragraph style and character style. To discover the power of styles, read the Writer Guide.
When a border is thus set, it becomes a property of the paragraph or sequence of words. Pasting a picture will not distort the border.
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