I am about to purchase a .com domain directly from its owner.
How relevant is it that domain registration expires in 7 weeks? Should I expect a renewal fee even if I purchase before? If so, which registrar should I go for to reduce the fee?
How relevant is it that domain registration expires in 7 weeks?
Not much, except if the acquisition process starts to last many weeks...
.com has no contact (for now) at registry. A change of owner/registrant is something that will happen only through the current registrar, internally of it. Hence this will just by itself not change the expiration date, except if the purchase process includes a renewal.
Of course if you do a transfer between two registrars, the fact of doing a transfer will extend the expiration date. But this has nothing to do with the registrant change.
One way wish to never wait for the last time to make renewals. It makes basically no sense since in most of TLDs (but not all; at least in all gTLDs) a renewal can happen at any time and will extend the current expiration date, so the end result does not depend on when you do it. But waiting for the last time may bring you problems.
You should make sure to understand fully what you pay and plan accordingly: do you pay just for the registrant change? Is a renewal fee included or not? etc.
Should I expect a renewal fee even if I purchase before?
Depends how the registrant change is processed, see above. So that is a question for current owner of the domain and/or the company used to do the acquisition.
If so, which registrar should I go for to reduce the fee?
I am pretty sure the price you will pay for the domain will be higher than the renewal price, so there may not be a good value of your time to do that.
Once the domain is in your end, you can transfer it to any registrar of your choice. The transfer will extend its expiration data by 1 year.
Also, picking registrars solely based on their price may not be a good long term choice, there are other aspects that may seem irrelevant at the moment but when you need them you can feel pain if problems. Examples: how is security enforced (if you acquire an high value domain name I am pretty sure you want it to be secured), see the recent announcement of data breach at 3 major registrars, or how easy it is to transfer out of it, or how the customer service responds (both in quality and speed), etc.