Does a 3 phase motor have to be inverter duty to be operated by a vfd?
No. Many of us us VFD's with loads of non-Inverter Duty motors. No problem. The long answer is that 'Inverter Duty' means more insulation to handle voltage spikes that can accrue with VFD's. Insulation is always good, but I wouldn't worry about it in a non-critical/non-production environment.
The motor I am looking at has "Reconn" listed beside rotation, Does this mean I will be able to use it in forward and reverse with a vfd?
VFD's can do forward/reverse with ANY standard 3-phase motor. 3-phase is simple...swap any pair of leads and you get reverse. VFD's do this. (I don't know what Reconn means and it doesn't matter to your question). (note, some odd VFD's like the KBAC may require you to buy the optional switch on your VFD to switch to reverse...most other vfd's let you select direction as an option on the screen).
Do you need a vfd with a rating of more power than the motor? I'm sorry for all the questions lately but I need some guidance here.
To answer this we need to know what exactly you want to do AND which VFD model you are looking at. VFD's were originally designed for people to control the speed on motors -- NOT to change phase or voltage. Nowadays, we all use them to take our 110v or 220v 1-phase household power and turn it into 3-phase 220v power in addition to variable speed.
Older VFD's often needed to be de-rated (you need a bigger VFD) if you wanted to use them to generate 3-phase power from your 1-phase power. HOWEVER, the KBAC and TECO VFD's that many of us use do NOT have to be de-rated. Just choose one that will take whatever household power you want to use (probably 220v 1-phase) and outputs 220v 3-phase, and use the rating it suggests for motor hp (so if it says it's rated for 1.5hp, then you can use it with ANY motor UP TO 1.5hp).
Technically, a good VFD nowadays can actually be used with a larger hp motor than it's rated for, and it will use its electronics to only give you the rated power. So if you buy a 1.5hp VFD and use it on a 3hp motor, this will work, but your 3hp motor will only output 1.5hp.
If some of this doesn't make sense, then just ask. Some of the explanation above was a simplification... tell us exactly what power you have in your shop and what you want to do and we can be more specific.