Do suspensions have a lasting effect/outlook on my account?

Unless overturned, a suspension is a part of your permanent SG record.
You'll have to file with your local law enforcement agency, you won't be allowed within 500 yards of SGTools giveaways, and it will lead to problems acquiring gainful employment down the road.

Just don't do it again, right?

In your particular case, you could just buy the game and activate it on your account. Problem solved.

If you are talking about an unactivated win, it doesn't have a big effect on your account. If someone creates an invite only giveaway to post in the discussions and they choose to use the sgtools rules checker to not allow people to enter that have broken rules, you will not be allowed to enter that specific giveaway. Also, if anyone checks your account on sgtools, they will be able to see the unactivated win, but that is all.

If you activate a copy of the game on your account at any time in the future, this broken rule will disappear from view and nobody except SG support will be able to see that it happened. You will also be able to enter the invite only giveaways again that people choose to not allow rule breakers to enter because you fixed the issue. Nobody except SG support can see that you have been suspended in the past, there is no public record.

Other than that, the only affect it will have is that if you continue to break rules in the future, SG support will see the history of broken rules and may decide to permanently ban you, but if you don't plan to keep breaking rules, that shouldn't be an issue.

Edit: One other thing I forgot. If you win a giveaway and it has been less than 30 days since the unactivated win, the giveaway creator can choose to request a new winner if they want to. They would need to manually check for unactivated wins to notice through because the site doesn't automatically tell them.

You have a number of options here as others have stated.

1. Buy the game and activate on account will solve it.
2. Send a message to the giveaway creator saying that the key given was for a beta version and ask politely for the full version of the game or ask them to delete that portion of their giveaway as the key was incorrect. If they don't respond or decline to do this after some time (a week should be sufficient), send a ticket to SG support requesting change of feedback to not received and take screenshots to show you tried to contact them to resolve this issue. You can also go to your history of license/key activations on steam and you should be able to find when the beta key was activated. If its around the time the giveaway was made, the SG mods may take it into account as to what you are saying is the correct version of events.

With regards to help you to prevent falling into the same trap again, firstly check to make sure the key you activate is exactly the same appid as the one on the giveaway. I also use sgtools to sync my account and check to make sure my account is clean and my wins have been activated as i have made the same mistakes you have. You account will not be impacted severely if it's your first time but multiple infractions will. I don't have a key for the game in question so i cannot help you out on this occasion so best of luck to you.