Max, you can definitely do the bulk of the work yourself. The bulk of the work can be done without specialized tools (mount indoor and outdoor units, run electrical, run piping). The difficulty is finding an HVAC guy to do the last 3rd of the job. That would be adding the flares to the lines, pressure test, pull a deep vac and release the refrigerant (or adjust the fill if needed). It's those last steps that require an investment in more specialized tools and may not be worth a DIY, but if you were to do it, figure $500-600 in tools and supplies. You have to be careful with the warranty if you go this route. Some manufacturers are fine as long as a certified tech does the final part of the install, some get persnickety about this.
One of the things I liked about Fujitsu is they specified a range of length for the linesets (16-60ft or something like that). I have no idea how, as most others specific a narrow range or absolute value and provide and adjustment in oz of refrigerant to be added or pulled out. None of this matters if you're paying someone for the final install, but for DIY, it can mean you never need to open the system. You just connect the lines, open the valve on the outdoor unit to release the refrigerant and you're done. But with a Fujitsu you will lose the warranty if you're DIYing. I went this route 6 years ago, no regrets, but it's not for everyone.