The first thing to note is that if you want to make the change without consuming any of this tax year's ISA allowance you must select a new account which allows transfer in and make sure you follow the new provider's transfer process. All providers must allow transfer out but processing transfers in is optional so not all providers do it for all accounts.
Second is that you should determine whether your existing provider levies any charges or place any restrictions on transferring out. My experience has been that cash ISA providers do not do this (I assume from your mention of interest rates that we're talking about cash ISAs) but it doesn't hurt to check.
When choosing the new account it's up to you to decide what features are important. If a regular payment facility via standing order or otherwise matters to you then check for that. Likewise if you want internet access to your account (there are still phone/post/branch only accounts out there). If this is money you expect not to need you may be able to get a better rate by going for a fixed rate over a couple of years.
One thing to watch out for is bonuses. It's common for a rate to have a bonus applied for a year, so in 12 months you might find yourself in the same position when your account suddenly becomes uncompetitive. This isn't a huge problem if you're prepared to transfer again, but if you want an account you can forget about then you might be better going for a slightly lower rate without any bonuses.