Hi WSO, I want to give back to WSO after using this website and many other resources to move from PubFin to Equity Research. Feel free to ask me questions and I will get back to them as soon as I can. I am by no means an expert (less than 1 year in ER) but I can add my insight into the industry and give advice to WSOers trying to break into the industry.
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Those are a lot of questions, but I'll take a stab at it.
It will be challenging to move from munis to equity research. Most ER candidates have a background in finance/accounting in the coverage industry for which they are applying or have prior experience in ER. For that reason, you will have to have superior technical skills and a good "story." Have a story that proves you understand the industry and would kill to break into it. Also, you need well-thought-out responses to behavioral questions (e.g. why are you moving from munis to ER?).
To strengthen my technical skills, I completed a self-study financial modeling course (e.g. BIWS), practiced modeling companies of my interest and signed up for the CFA. In equity research, modeling is typically only about ~10-15% of the job (depends on your analyst), but it is a great skill to have and will significant help you on interviews. As I said earlier, since your background is in munis you will have to be especially strong on the technical side. There are no shortcuts mastering technicals and simply watching YouTube videos or reading a few articles will not suffice. Investing in a course was the best decision I made. Also, I am now a CFA Level II Candidate, so I would be happy any questions relating to study prep. Warning: completing the modeling course and taking the CFA Level I is a huge commitment so be prepared to have no weekends and limited sleep. If it were easy, everyone would do it.
For networking, I cold-called and e-mailed associates and analysts non-stop. I made it a priority to email 5-10 people in the industry per day. Keep it short and simple. No one (especially in ER or IB) has time to read about your life-story (and nobody cares). Ask for a 15 minute call or a quick cup of coffee. The smaller the commitment, the better.
Persistence is key... it took me 9 months to break into the industry and I would consider myself fairly lucky. If you really want it, you will find a way.
I wanted to work in ER because the fast-paced learning environment, the skill set you develop as an associate, the excitement of public markets and following multinational corporations and the exit ops (e.g. buy-side or corporate development). Also, I would be more than happy with a long-term career in sell-side ER (unlike IB in which case I would be three years and out).
First off, congrats on the transition. With enough ambition, you should not have a problem moving to ER. Second, I can't fairly answer that question because I have only used BIWS. I can say however that BIWS was easy to understand, comprehensive and fairly cheap. It covers everything from simple accounting to merger and LBO modeling. I would highly recommend it to anyone interested in breaking into "high-level" finance (IB, ER, etc.). I am sure the WSP courses are awesome as well and friends have spoken highly of them, but I have never personally used them.