A starter on a Baritone is a novel concept (I was certain we all evolved to Baritone if we played them) but they are great instruments. I play mine daily- in fact, it is my go to, but I have a heck of a time not buzzing chords on it sometimes because I have short fingers (which is why I am not a guitar player...but I have one and I will get it!). I am going to assume you are in this boat, because you like the guitar sound, but you are here asking about Ukuleles
In any event- I would recommend new or Luthier conditioned vintage, because if you get a uke off Ebay, chances are it will need work that you do not yet know it needs...frustrating when you know you are doing it right and it is not sounding right.
That said- the old adage around here (which rings true when you are learning) is to buy as much uke as possible. There are several Bari's in your price range that I think are great IF THEY ARE SET UP. Kala makes the Makala Baritone for $70 and while I do not have one of these, I have a Soprano and a Tenor made under this bdget mark in my classroom and they are fantastic (and take a beating). Kala also makes the KA-B ($118), which is nicer in terms of appointments, but having played it next to a Makala...I would go Makala and play it into sawdust. The one I bought is a Kala KA-SB which is just above $150...I did not want to spend it at the time, but it sounded so great I fell in love with it...and it is sexy. Great tone from spruce tops if that is what you are into- they ring forever and have a lot of punch. That extra $30 buys you a solid top, which makes a better sound- it is all in the ears of the beholder though really.
Ohana makes a BK-10 model, which is all laminate (and on par with the less expensive Kala's) for $139. I have not played one, but do have an Ohana Uke, so I imagine it is similar quality. I was disappointed with the finish on my Ohana, but it is my other daily and is on my lap right now...in fact, I have not gone anywhere without it in six months.
I don't own one of these, but there is a fellow on here who swears by them (and is highly credible).
Rogue Baritone...ugly as sin, but if you hate Ukulele, you aren't out much money. You are definitely going to learn set up with it as at that price no one is going to do it for you...PM me, I can help.
Again, set up and strings are the most important part of the equation here. I thought I would never tune my Baritone like a standard Ukulele until I got some strings from Southcoast...and this goes to the sound you are looking for and playability so bare with me. My Baritone is now tuned Low G (GCea) instead of DGBE (like the bottom four of a guitar- standard for Baritone Uke) for many reasons. First, it still booms when it is not tuned re-entrant (Uke's normally have the lowest note as the second string....this may be what your ear does not like about standard ukes...it drives my dad CRAZY), AND because I play with my wife a lot. SHe learns a little slower than I do, and she cheats and looks at my hands. It came to the point of not being able to play my favorite Uke because my hands and her hands were doing two different things.
This may be a problem for you...if you learn by watching. If you have a standard tuned Baritone Ukulele, you are not doing what everyone else is doing (if you have folks to play with). This is the caveat here- Tenor Ukulele, or a Baritone tuned GCEA, will open up your learning opportunities. All the books are written to this tuning, everyone on the YouTube is playing this tuning...other ukers are tuned to this. At the end of the day, it is easier, unless you are an advanced player, to learn on this tuning, and with Low G as an option (only one kind of strings available for Baritone in this tuning, but they are great strings)...it will still boom.
Hope that makes sense,
Dave