What is the best way to redirect a domain ,say www.example1.com,to another domain name ,www.example.com ?

I'm also wondering where you see the reference to an actual forward when you setup forwarding. In my experience, the forward happens immediately and without any reference that it is happening. That said, you ARE able to host more than one domain name from one location on a hosting server. If you were hosting with Go Daddy, you would set up an 'alias' to accommodate this. However, since you're using another hosting provider, you'll need to ask them how you can apply additional names to your hosting space.

For SEO purposes a 301 permanent redirect script, in the majority of servers that could go in the .htaccess file of the old site, if the old site has a useful number of backlinks you could redirect each individual page to it's counterpart on the new site, otherwise you may be able to setup a domain redirect at your registrar, eliminating the name server and redirect script hosting needs.

if you are not sure how to do .htacess or don't want to host the site

sign up for cloud flare

point your name servers to the ones cloud flare gives you

then point *.example.com to another domain or IP Address

Most of the CPanel have already redirect options which you should avail.