I noticed that the OP is from the US so I will do my standard advice
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spend some $ on renting equipment and do your own testing.
I have used Lensrentals.com from Tennessee and there are other companies as well.
LR sends you your selection by Fed Ex and you return the stuff the same way, get the max protection insurance they offer. If you know you will be using them at least 3 times in a year, it may pay to pay for their special membership and save money on shipping.
they are good at giving advice as well, email or call them
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be sure to check out the reviews:
Pentax Lenses - Pentax Lens Reviews & Lens Database
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then decide what you want to buy
figure out if you want new or " experienced " and if " experienced " check out the forum's Market Place ( " buy/sell "
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I would look at the D FA 70-200mm F2.8 or the D FA 150-450mm zooms both heavy but can be used hand held
zoom might be better with kids sports unless you know you won't be close to the action
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primes, I like my DA * 300mm I have no experience with the 200mm
I also like my HD DA 1.4 rear converter but has been stated you do lose a F stop ( more ? ) if you use it.
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have fun, ask questions
and please post the photos when you are done