Yes handloading will improve accuracy, so will practice.
How much accuracy do you need or want?
What distances are you intending to shoot over?
Handloading is only cheaper if you shoot a lot of rounds, recycling your brass.
How many rounds per year do you think you'll shoot?
My son & I started fullbore FTR target shooting with an off the shelf Savage Model 12 .223 (26" 1:7 barrel).
With handloads (80gr A-Max, in Norma cases with ADI2208 powder) it was competitive with 308s in short - mid range (300 - 600 yards) except in strong winds. It was competitive in light winds out to 1000 yards.
The 223s issues with wind strength meant we moved onto 308s for target shooting.
If you know your needs it can help define your answer.
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