I expect to live in the area for about 3 to 4 years which makes me think that renting might not be the best answer.
The threshold here is five years. So if this were all, you would be better off renting. The reason is that within five years, the closing costs will eat up all your equity.
My plan is to buy an inexpensive home in under average conditions and fix it up to increase its value.
So buy a home. Improve it. Live in it. Then sell (flip) it. That could work, even with the three to four year time frame being less than the five year threshold. That's because the higher selling price may offset the closing cost losses.
This is the situation for which a five-year adjustable rate mortgage with a balloon payment at the end is designed.
Some issues to consider:
Do you actually have any experience at this? It's quite possible to lose money due to selecting the wrong house, making the wrong changes, or hiring the wrong contractor. In general, I wouldn't recommend this approach unless you plan on doing it repeatedly. The reason being that if something goes wrong, that's a learning experience for someone doing this repeatedly. But it's a major financial hit for no gain for someone just doing this once.
Are you sure that the local market in three to four years will be as good as the market now? For example, if you had done this in Miami or Las Vegas in 2006, your property would have likely lost half its value if you tried to sell in 2009.
What will you do if you lose your job? If renting, your worst case is breaking your lease. But if you own, you may be stuck paying a mortgage on a property where no one is living (e.g. if you moved to a different city to get another job).
It is possible to make very good returns with this kind of plan. But it is also possible to take big losses. That risk is part of why the potential gains are high.