There are many points to compare.
First as you are going to sit very near to screen, Plasma are not good bet, as they produce maximum UV rays in all, moreover they product a lot of heat compared to others. Also the technology designed behind plasma is old and hence you will get lesser performance and features then others.
Second LED TV's are better then plasma, they product lesser UV rays and hence lesser fatigue on your eyes and brain as compared to plasma. They are designed to support the best resolution and functions.
But in Plama an LED the light is emitted from screen to your eyes, hence fatigue level in them is much higher compared to projectors, where it is totally opposite, hence fatigue level is much much lesser.
I totally agree to what Eternal Champion said, projectors are not good for short distance watching, but I will like to say probably my friend forget to take in consideration latest short throw smart LED projectors. Eternal Champion is perfectly correct about conventional lamp projector it needs long distance to project images, which you don't have. Also I totally agree to Lmah, this conventional projector's lamp will cost a bomb like $600 or the lamp cost differ on which projector model you are comparing but generally very high costs.
The Best I suggest is to go with latest Smart LED Projectors which are designed for Home Cinema purpose. It has many many positives....
1. Short Throw - so you can get 60~62inches screen size by keeping projector at distance of 170~175cms away from screen.
2. LED - hence you get a very long life on lamp for example if you watch for 7 hours daily, no lamp change till 10years. Good quality LED Projector give 20k LED lamp life.
3. Smart - This kind of projectors have Android OS inside and supports many features like watching Youtube or other videos online. Sorry forget to say these types have wifi, BT 4, USD3 , 3 hdmi and can do many many things for you. It is same like comparing old generation mobile phone and new generation smart phone, just image........same way smart projectors can make the device many time more productive and can be used for many many purposes.
4. Gaming - Suppose during week end you plan for gaming with your friends, then ??? These new generation projectors are palm size and easy to carry and have the best hdmi v 1.4, which support maximum data transfer rate and hence no lag in games.
5. Active 3D - 3D is future and if you buy a device which don't have 3D then you will curse yourself in some time. This projector have Active 3D the best and most evolved 3D technology globally, developed by TI in US. If you have never experienced this 3D, then buddy let me tell you, you have not seen the real 3D
If I will be in your place and surely I will look at best performance, less eyes straining, moderate cost, mobility, 3D and smart features, in short I will go with product which has all.
I suggest check out Luxcine z2000sd model projector, you can search on YouTube.
Check their company YouTube Channel :
http/www.youtube.com/user/3dProjectors/about
You can check pricing here :
http/www.aliexpress.com/store/300840
If need any further help, hit me back..