The Contessa 26 is probably a good choice, if you're planning on going bluewater. The Alberg 30 is also a pretty good choice, as are many of the Cape Dory series of boats.
I would get and read John Vigor's 20 Small Boats to Take you Anywhere
Almost any of the boats there would be a good choice, but I don't know how many will be in your price range...however, it gives you someplace to start.
I would highly recommend that you reserve about 15-20% of your total budget for re-fitting, upgrading or repairing whatever boat you plan on purchasing. This means that you should probably spend a maximum of about $15000 for the boat and save $5000 for the survey and re-fitting.
All boats are a work in progress, and it is almost impossible to get one that you will find perfect for you in every way. You will probably find that any boat you do end up purchasing will need to be modified in some way to make it more suitable to what you will be doing with it.
As monohulls go, I like the Cape Dory 25D, the Contessa 26/32 and one person I know just bought an Alberg 30, which looks to be a pretty solid boat as well. All three of these are listed among John's 20 selected boats.
Wheel steering is a bit rare on most smaller older boats, which are generally designed with a tiller in mind. Wheel steering adds complications, and multiple points of failure, as well as often reduces the effective usable cockpit space on these smaller boats. Some of them have been retrofitted with wheel steering, but it is generally problematic, adds weight and complexity, and reduces space on what is already a space limited boat.
I find it strange that you're willing to say that you don't mind having an older boat, yet aren't willing to invest some serious time, effort and money into making whatever boat you get seaworthy and comfortable to handle. Given your goals, sailing from Vancouver to Mexico, Latin America, and Florida....you will probably need to tweak the boat setup and layout a fair bit.
Here's a quick search of YBW.com
for some possibilities. An Alberg 30 is one of the first dozen listed.