Why don't you go for power and accuracy? You don't have to sacrifice one to get the other.
But... I would recommend the "precision TM chamber" as your first drop in part. This is $60 and comes with a barrel. To save money, you should stick with that. Then, make some barrel spacers out of electrical tape to cut down on barrel vibrations.
Then get a nice VSR firefly bucking, it's $20, but worth it.
With your last $120, get a hotter spring and a bearing spring guide. Laylax parts will be $50 for these pieces, other brands will be cheaper...
Now, with your remaining $70, get some Deepfire reinforced sears for the VSR stock trigger mech. These are strong, but 45* sears, so you still can't run super powerful springs. Your trigger pull will be hard also if you go for a really heavy spring. These run $50 last time I checked. Might be a little more expensive, I forget.
For that remaining $20, buy yourself some nice bb's.