Is there hope for you? Absolutely!! I've seen far worse bites treated to give really wonderful results!
Invisalign does work, but not for every case. There are things it does well, things it does successfully sometimes, but fails at for other people, and things it cannot realistically do at all. This means that some people are not candidates for Invisalign, and others who are borderline might end up with less than satisfactory results and need to go into fixed braces if they want things right.
I am not a dental professional, but it looks like you have a significant overjet (a lot of people get this confused with an overbite, but an overbite is when the upper front teeth close too deeply over the lower front teeth and hide them - sometimes the lower front teeth even bite into the upper gums!) - an overjet is when the upper front teeth are too far in front of the lower front teeth, so that they can't work together like scissors when biting into food. An overjet can sometimes be treated just using rubber bands with braces - and this is possible, though an advanced technique with Invisalign, so not all docs would do it, and it may not be successful. Sometimes an overjet can be corrected and give nice results by extracting teeth (usually premolars - also called bicuspids - they are the fourth and fifth teeth back from the middle) but for other people that would give a result that would not look good. And sometimes to correct an overjet requires surgery on the jaw.
The gap between those lower teeth might cause trouble for invisalign - closing gaps is something it does with poor predictability, because sometimes the teeth will just lean over into the gap instead of moving along to close the space. Attachments placed on the teeth (they are removed at the end of treatment, or sometimes sooner) to match little "bubbles" in the Invisalign trays can help prevent this, but it doesn't always work.
And of course, since I am not a dentist or orthodontist, there may be other issues I am totally missing picking up on.
My advice to you is to ask your dentist to recommend a good orthodontist, and head in for a consultation. And, especially if either extractions or surgery are suggested, consider also seeking a second opinion from another ortho. As Mariah and Stephanie have suggested, do consider fixed braces as a possible option - there are various types of bracket available today that are very discreet in appearance, including ceramics. (By the way, not all orthodontists will place ceramics on the lower teeth, since they are extremely hard - harder than metal brackets - and can pose some risk of chipping the upper front teeth as a result)
Oh, and I've never heard of it being a necessity to have the wisdom teeth extracted to have nvisalign. I am not sure where your friend got that impression.
Best wishes.
Albert