There are probably 20 different ways to get to mid 9's and no matter what your budget is, it will cost more than you plan. I think $20K probably won't get you to mid 9's. 30K maybe if you follow the advice of those who have been there with a proven combo. I'm at $40K in a low 9 second bulletproof stage car and I do 99% of my own work. I could have done it cheaper if I hadn't tried to be cheap in the begining.
You have a lot of paths you can follow on the V6.
1. You can get there by buying cheap parts that are marginally good to mid 9's. You'll have a car that either has issues everytime you play with it or you will be too afraid to take it out at the risk of breaking it. For the most part, you'll spend more money in labor making the cheap parts work that you would to just buy the good parts the first time.
2. You can try to nickle and dime it by chasing good parts either used or at a discount. This takes twice as long and in the end you'll spend more because half the used parts you buy will be bad before you even see them. This is very frustrating and I tried to do this for a long time, until I learned my lesson.
3. The best way to do it is buy the best quality parts you can find. You'll buy parts once and you will have confidence in them. Your budget will dictate how fast you can go, but in the end you'll save money. That's hard to learn any other way on your own, but it's true. The other plus to buying good parts, is that when it's all together, you'll have no issue paying top dollar to have someone tune it. This is the single most important part and can make or break how you enjoy the car.
You can go the LS route, but in the end you'll have a mid 9 second car with a junk yard motor that has very little resale value. Everybody thinks you can put an LS in your car and run 9's and do it all for little money. So even after you've spent twice as much as you though putting the LS in, you won't be able to sell it because the potential buyers think it can be built cheaper. For all the guys you hear of having sucess with a junkyard 5.3 going 8's there are twice as many that broke something running 10's. If your building a complete car, the motor is only half the cost, so you really won't save much in the big picture. Not that it matters for a mid 9 second build, but over 1000hp, the LS and the V6 cost the same.