My 2 cents from my own story.
I wasn't looking for a solo opportunity, but when I interviewed in my eventual area, the opportunity was too good to pass up. I was offered a guarantee by the hospital, although I was to be a solo guy--not salaried by the hospital. They cover me for a year and I pay them back with time for loan forgiveness. IMO, that is really the only way to do this unless you have significant cash resources. I didn't.
Benefits v Risks of solo: You're the boss. I cannot tell you what a huge amount of freedom that brings. I love it. You get all benefit, but you do take all the risks. It's sink or swim. You blow a case in your first month in a big way, and you're toast. Being the boss means the office is yours to design, run, change, and invest in how you see fit. The drawback is you've got to learn business. If you don't learn business you're a gonner unless you get lucky and have enough cash on hand to get a well-experienced office manager who can do all that for you. Still you need to learn it so they don't take you for a ride, something that happens far too often. Be prepared to skimp. Also be prepared to be scared out of your mind for a few months until your rep allows your referrals to build. Market, Market, Market your practice. ALWAYS be available. NEVER say no to anyone or any referral--even if you'll lose money on the visit. This will buy you loyalty from the PCP. Make absolutely sure your consultation note is exceptionally well written and thankful to the referring doc. If you have good notes, they'll love it. Make the patient feel like they've got your undivided attention and the best care available. NOTHING will make or break your practice more than word of mouth--especially when the pt reports back to the PCP.
As far as hospital employee situations go. You trade security for freedom. For me, I'd never go that route. You'll be a ***** for an administration that could care less about you. This is less true in an academic setting. I may sound harsh in my summary of this route, but as more and more docs do this, I see more and more docs who get screwed in some way about it. It definitely provides security in the face of declining reimbursement, but you also end up having to tow the party line whether you agree with it or not. I've seen a significant number of docs pull out of their hospital-owned practice for this reason.
As far as joining a group, what you get is less freedom--you'll be an employee for a year or two usually. You'll be told how the practice works and have little input into changing much about it, at least from an administrative standpoint. However, you'll build a busy practice far faster, you'll have a more secured income. You'll have access (hopefully) to more extravagant equipment than you could secure on your own. You'll have a built-in referral network, built-in staff, built-in insurance network. All of these have their own ups and downs.
As far as Academics goes, let's just say that could vary so widely between institutions I can't even begin to address it.
Having a mixed practice is possible. Many people do it. I did it for 3 years while I was in the Air Force. You're never fully accepted as a "faculty" member, but you do tend to find the residents like you more than their own--at least I did. I was much less malignant to them and let them be primary far more often. Also, I didn't make them do all my scut work. Mostly because I didn't trust them enough. I had enough misses from jr residents as a chief, that I double check everything anyway. I enjoyed that and miss it a lot.
Now, after only having a solo practice for a short time, I am merging with another practice. Two reasons. First, is to improve market competition. The person I'm joining with is, in mine and many other opinions, the most well-respected ENT around me in terms of quality of care. We graduated at the same time and practice very similar styles and our likes and dislikes in terms of surgeries and interests compliment each other well. Second, is security. We both would like to share call and share cases. We both would like to secure referral patterns and feel our reptutations will lock that up nicely together. We'd like to be able to share pt care more efficiently. If there is something I do well, I'll take the pt. If there's something I don't do well, I'll have a partner who can take up my slack. Patients get the best care that way without losing out on financial benefits.
So, I started solo and love it. However, to really grow, particularly in the market I'm in, I found a wonderful opportunity to merge which will only further my practice and as a nice corollary my earning potential. If this particular doc wasn't so awesome, I doubt I'd be getting a partner so quickly. In fact, I've turned 2 down this year for that reason.
So that's my 2 cents. Or 2 bucks as it turns out.