Client or freelancer? Do I send a payment link to him or does the client reimburse me later?
That's completely up to you, and what risks you're willing to take.
Because my freelancing philosophy is that I consider myself the product I have no reason to sell anything else (hosting, domains, other freelancers' time).
Instead, I'll manage all those resources for a client, but bill the way I always do: charging for my time.
Just realize that if you do sell those things to clients (reselling a hosting provider's services) you inherit the responsibility the client would otherwise associate with the hosting company. Since you're the one they're paying, you're the one they'll contact for support.
While hosting companies have entire departments dedicated to this, you probably don't.
or the client reimburses me later
That's perhaps the worst situation, where you're not even making a profit on reselling a service. In this case the client might not hold you responsible for any problems (but could, since they're still paying you); however, you're on the hook for the payment should they not reimburse you.
That'd be a situation to avoid completely.
In your case I'd help the client setup the hosting they need (charging for your time to do that). Then if they have you on a longer term contract, make sure you're CC'd on all account emails, and manage as much of that for them as possible, but keep the business relationship between your client and the hosting provider.
It depends on the sort of business relationship you want with the client and whether the client is knowledgeable enough to manage things by themselves or basically needs someone to do everything for them.
Sometimes it makes sense to merely create and deliver the website, get paid and move on. If the client experiences problems or wants enhancements, they may or may not contact you again.
If you want longer relationships with clients, it could make sense that you - for a fee - provide hosting in a kind of 'all inclusive' package. The benefits would be a constant stream of money and a tighter binding to the client who would probably consider you a preferred partner. The downsides could be that you will be blamed for hosting problems that are out of your control.
You could consider a reseller package from your go-to host but from my own experience it's best to let the client contract the domain/hosting company.
If you do want to resell, you have to take in account the responsibilities you'll have towards to both the hostingcompany for payment aswell as your client for downtime.
If you're not getting paid for this responsibilty/risk you could straighten it out with other costs, but why not skip this burden and show your honesty by pointing them to the best host while asking no commission over that sale?
The only case you should do it, is when specifically asked by the client and you both agree on a sum which comes with your calculated risk.
If you are BUILDING the site, put it on your own servers first unless the client is paying up front. There are too many freelancers who are on this site complaining about how they've been burned because they did work on the client's servers and "hoped" for payment at the end. Stupid! Don't be one of these people.