A couple of thoughts.
If you want Marshall (who has been my first choice for more than 5 years), it will take a supreme effort and even then I would consider it unlikely.
IMO what you need to do is go to him immediately after his season ended and have everything layed out. # years, salary (probably have to start at $3MM yr - doubt he would consider much less than that), your vision for the future of the program, how you see him fitting in.
Then you let him make a decision.
In general, you need to have one big name guy that you think is interested (whether it be Marshall, Smart, Wright, whoever) you go to them with the full package ready to go. Then wait for the decision. If they say yes you get to move, if not, you then immediately go to the next group of coaches on your list. You can't have more than 1 big name - it takes too much time and then the solid 2nd choice guys take other offers before you get to talk to them. You will only get a chance at 1 A-list guy, so you have to know who you want and be ready to move.
I also wanted to comment on type of play that has been brought up here. I'm not sure you want a team that plays 'fast'. It works the same in basketball as in football. If you look at the teams that have a high tempo it includes UNC, Duke, L'ville. Teams that are loaded with McD's and high 4-stars. UVA is the second slowest tempo team in Div 1 basketball. ND is a slow team, Miami is a low tempo team. NC ST is in the middle. Generally the more talent you have the faster you play in order to create more possessions. I don't think GT has to play as slow as UVA or ND, but it shouldn't be looking to run a fast tempo like UNC or Duke either.
FWIW, Marshall runs a very slow tempo. His numbers are pretty similar to UVA.
A couple of coaching thoughts. I have a list, but will refrain from talking about it until Feb when it should become apparent if Gregory is going to not return.
White's father is Duke's AD. White is on my list, but probably not in my top 3.
Josh Pastner is basically the white Paul Hewitt. Recruits really well, team plays fast and undisciplined.
RamblinRed