Some people have given good answers for when you are applying to mid-to-large sized companies, so I'll give some input in case you are interviewing for a position in a small company.
First, there's hardly space for "diversity" in a small company. The sample size is just too small to be "diverse". Trans people accounted for 0.6% of U.S. adults. So, a company with 20 people selected at random from US adults has 88.6% chance of having no trans people there. And possibly many of the people working there have no close relationships with trans people. That being said, for the same company, there is a 60% chance that there would be some LGBT person in it. The chance for LGBT falls to 37% if the number of random employees was 10.
Given the fact that many companies start with a group of non-diverse friends (neighbors, college mates, family), chances are skewed that you are more likely to find companies with either no LGBT people or just LGBT people than what they would be if choices were random.
That does not mean you are going to find unwelcoming people. I believe most adults in the workspace are well aware that some prejudices should stay in the past, and that diversity should come naturally as a company grows, hence most reasonable people have the acceptance part sorted out.
What you may find is that some people are just not ready or used to deal with LGBT people, and a sane manager will expect you to have some degree of tolerance to this. For any person at all, some good quota of tolerance is required. So, if I'm interviewing you for a position in a small company, I'd like to know that you will not throw a tantrum every time some mentions a common misconception about LGBT people. I'd like to see that you will know how to keep your temper and leave clarifications for a personal conversation with a non-intentional offender. Know when and how to ask for help from a manager or to seek HR is also something I'd like to see but saying you may need advice on these also looks like a good sign to me.
In short, just don't be the snowflake that gets in trouble with everyone else and plays the discrimination card and you should be fine on your end.
All that being said, as others mentioned, no hiring manager would acknowledge that their company is LGBT unfriendly, yet those companies exist. For the sake of your mental health, you should avoid working on one of these as much as financially viable for you. As gnasher suggested I'd second that you should be upfront with your plans, preferably at the job interview if you can afford to lose a few opportunities. The manner in which the interviewer will react should tell you a lot. The actions he/she considers afterwards will tell much more. Remember the tolerance part, so don't judge if the person looks scared of what you are describing or if they ask dumb or borderline offensive questions. An example that comes to mind: "Are you sure you are going to do this? That is very drastic!", just give a polite answer such as "Yes, I've been planning this for X years, and now is really the moment where I get the best result/benefit for a fair cost and risk". Consider that ignorance can be remedied if you communicate well and the person is a good listener, but prejudice (whose signature is the unwillingness to listen) is a much harder wall to overcome.
Now, you should also think that the people hiring you know their staff... To some extent. If the company is filled with people who would have a hard time accommodating you, then I'd say myself it is not in anyone's best interest to pursue in hiring you. Discrimination may be against the law, but having coworkers who strongly dislike themselves for personal reasons is something that any company wants to avoid, especially at the starting point (i.e. job interview). And the preference lies with people already in the company not with the potential newcomers.
If during the interview, you see a good reaction to your transition plans, if they happen to mention similar situations in the company or with family (maybe ask up front if the person has already seen someone undergoing this process?), and if they reach out to you afterwards, then I'd bet you have a very good starting point at this company.
Asking for things like "LGBT groups", "Equal Opportunity Employer Office" or similar support organizations is likely unfruitful in a small company. Maybe you could propose starting one? If people do not have any notion of diversity, maybe there are some misconceptions that you could elucidate in a presentation to the company? The thing is just that small companies have much less structure for several things that big corporations are basically required to do. But being proactive, kind, and tolerant can help reshape the landscape of the company for a better future and growth.
Now regarding the options you've mentioned:
What if you don't mention it at all? You might prevent losing some opportunities, but they are likely at places you wouldn't enjoy in the long run. Up to you if the financial situation allows taking your time to find a better option. When you start transitioning, people will notice and have a hard time communicating if you resist or avoid communicating yourself.
What if you tell only after having a written proposal? Then you secure the job, but you'd still likely be on some probation period. That basically means that for a period of maybe three months you are still being closely watched, along with your colleagues to see if the cultural fit is working. Remember that the priority goes for the established employees, not for the probation period ones. The advantage here is that in some jobs particularly entry-level ones, "being nice" is about the only thing that matters, but now you've gained yourself an opportunity to show off work and deliveries. I'd work extra hard during this probation if you caught people by surprise with news of your transitions. As for communicating, remember to communicate well your intentions with your peers, this gives them time to adjust, and the more your colleagues feel comfortable talking to you, the better you can sort through social issues.