As a plan provider, I cannot make a specific recommendation as to a company to work with per BP guidelines.
What I can help you do, however, is refine your question.
Self-directed IRA's come in several formats offered by different types of companies. The type of self-directed IRA that will best suit your situation and goals will drive the process of identifying the right firm to work with.
A self-directed IRA custodian is a processing entity. Think E*Trade or Fidelity with different paperwork. All IRA based plans are required to have a custodian to administer and report on the account. What makes a self-directed IRA custodian different is that they are not purely connected to the public exchanges and limited to investing in stocks, bonds and funds, but rather have the staff training and paperwork to document the IRA's investment in the more individualized transactions that occur when investing in real estate, notes and other non-traditional assets. Such custodians will hold funds, sign documents, issue expenses and receive income on behalf of your IRA and act as your processing layer. This works OK for relatively static and simple investments like a private placement or crowdfund, but can become rather cumbersome and expensive with a more time sensitive and transaction intensive asset such as a rental property. You also need to be aware that custodians are passive in nature and simply process transactions at your direction. They do not provide meaningful oversight or guidance with respect to tax code compliance.
A checkbook IRA LLC is an enhancement on the above structure that is generally more time and cost efficient for investors with a more diverse portfolio. It starts with a self-directed IRA held by a custodian, but the IRA simply makes one investment into a specially designed LLC entity. The IRA owns the LLC, but you can be the non-owner manager of the LLC and have signing authority. This allows you to directly manage transactions via the LLC and eliminates the paperwork, processing delays and per-transaction fees of the custodian. These plans typically cost a bit more to establish due to the legal work, but in most cases will save you considerably over the long term. With a quality provider, such plans also come bundled with meaningful consulting guidance to help you get the most out of the program while staying inside the IRS guidelines.
A similar checkbook program is a Solo 401(k). Such plans are available to those who have some form of self-employment and no full time employees. As an owner-only business retirement plan, the Solo 401(k) has higher contribution limits, allowing you to build your savings on the front end as well as providing investment flexibility. The Solo 401(k) also has the advantage of being more favorable for real estate investments using debt-financing such as a mortgage - as the 401(k) is exempted from a small tax called UDFI that an IRA would pay on the percentage of income derived from the borrowed money.
So, as you continue your research and get feedback here on BP, think about what type of program will best suit your needs and be sure to ask questions along that line. Get on the phone and speak with a few of the providers that are active here on BP. You will pretty quickly be able to tell who is just selling something and who can become a valuable member of your team.