There are several ways to look at this. My first thought since you are just starting out is to apply the 3F rule, meaning it's going to be cheaper for you to rent. If something breaks on the rental, it is the schools responsibility to fix it. Worst case you lose a few days of training. If your plane breaks, your down until you can fix it
With that being said. If your heart is absolutely set on buying the plane use it, and do everything Part 61. About the only advantage of doing instrument 141 is it eliminates 5 hours of Sim Instrument and 50 hours of cross-country time, but it is 35 hours dual in a rented aircraft. By doing it part 61, your min time with a CFI is 15 hours. You build the other 25 with a safety pilot. Remember these are mins. You the quality of your CFI and you ability to grasp the material may be a little different. Then go and fly the wings off your plane until you get to about 230-240 hours total time, get your required 10 hours in a Complex/TAA aircraft and go take a check ride. You will be learning the commercial maneuvers in that 10-20 hours. Again this may vary, but you are only required 10 hours.
There are advantages to both. Go talk to some people in your area and see what training route they took, what they liked and didn't like. It may be applicable to you. Then make the decision that best fits your needs.