As you have admitted guilt to the offence, this is something you will need to disclose to the SRA.
Therefore, I would recommend applying for the suitability test now and at least start this process, if only to help you know an outcome on this earlier and to get it off of your mind as soon as possible. When you inform the firm is up to you - ultimately you would have to inform them if you didn't pass the suitability test and your offer would be rescinded as you couldn't meet the terms of your employment offer. However, if you were deemed to pass the assessment by the SRA, the firm would actually be in a bit of a dodgy situation if they retracted their offer based on your charge alone and if the SRA approved your ability to become a qualified lawyer.
You don't need a lawyer to undergo the suitability test. Many people will do it without one although there are some lawyers who can advise on this particular process. You will need as much information about the charge as possible. You should also line up character referees who are happy to back up that this is a one-off and out of character. Where possible the more "prestigious" or respected the person is (e.g. the type of job they have, the seniority of their job, how long they have known you etc) will all be important here.
I have known people with some pretty serious charges still be approved by the SRA, so based on the limited information you have provided, there is nothing that is overly concerning to me. However, it is hard to advise on how likely you are to get approved and it would actually be inappropriate of me to even attempt doing this.
I'd start by calling the SRA and getting as much information from them as possible as to what you should provide, what the timescales are etc, and then decide a course of action from there.
