Linotype is the foundry/licensee providing the digital font. The licensor of the font is ITC (International Typeface Corporation).
TTF is short for TrueType which is one of three standards for font formats used on personal computers. It is very popular on Windows systems because Mr. Gates licensed it from Apple (who actually developed and owns the standard) and included it for free at a time when Adobe still wanted to be paid for their Adobe Type Manager which is used to handle PostScript Type One fonts on Windows systems. Type One fonts were widely used on Mac systems and are the main standard used for digital type. The other one is Open Type.
The need for having ATM installed on a Windows system was eliminated with the release of Windows 2000 and higher so either format will work on your Win-PC if you have an operating system of any of those types.
Type One fonts are inherently higher in quality because most fonts are originally digitized in that standard and then converted to TrueType. The difference can be seen when the nodes are displayed. Simply put, TrueType has more nodes in their curves. For example, TrueType uses 8 nodes to define a circle while PostScript only needs 4 nodes.
Now that you've waded through that little dissertation, Inspire is a Windows application which should be able to access any font which is installed into the Windows operating system. TrueType will work for sure and Type One should work.