Given your rather spare budget, I would recommend you look for a smaller boat, say 30-35' LOA, but reserve about $10,000 of the $30,000 for refitting, upgrading and equipping whatever boat you decide to buy. I would look at James Baldwin's Boat List
for a "pocket" bluewater cruiser, rather than the list on this forum which focusses on mainly larger bluewater boats.
I would also highly recommend the two of you take at least a basic ASA 101 learn to sail course. Given that neither of you know how to sail, this is a requirement IMHO. I would also recommend you get whatever boat you're looking to make the voyage in and spend at least six months sailing her on coastal cruises and slowly getting to know the boat, and how she handles in different kinds of conditions.
What’s the best route to take? I’m in no rush.....
There are three routes you could possibly go. First is down to the Panama Canal and then out into the Caribbean and across the Atlantic. The second is around Cape Horn at the southern tip of South America and across the Atlantic to South Africa. The last is west across the Pacific and then through the Indian Ocean to Africa from the west side. Each of these has its difficulties and challenges, and each has its advantages/disadvantages.
What are the best requirements the boat should have...from initial investigation...head, shower, two double beds, solar, refrigeration, fresh water maker and the usual radios
, safety...what else? Don’t want to need for something I should have thought about before!
Most smaller boats aren't going to have a shower, then again, most smaller boats don't have the fresh water capacity to handle having a shower. If you're expecting to get a boat with an shower for your budget, you might really want to re-think things. It probably isn't going to be happening.
You don't want two double beds... again, you don't seem to understand what the situation is. What you'll need is two good sea berths. Sea berths, by their nature, have to be fairly narrow. Pilot or quarter berths would be excellent. Most smaller boats aren't going to have two full cabins either. The v-berth, which is the forward cabin will likely be relegated to stowage for the duration of the voyage, since sleeping in a v-berth on an ocean passage can be less than comfortable.
An RO watermaker would be a luxury, and I suggest not relying on it. You should always have sufficient water in tanks or jugs to last out the voyage. If you were thinking of making water as you go, that's not generally a safe idea.
Refrigeration is expensive on a small boat, and requires the boat to have battery banks far larger than would otherwise be necessary. It is not a necessity, and many long-distance cruisers do without it.
How long should I expect the journey to last if I decided to cross the Atlantic from Panama?
Unfortunately, sailboats are somewhat limited in their choices of passages they can make. If you were to look at the normal winds, a passage from Panama to South Africa would generally entail three partial crossings of the Atlantic ocean. You would go from Panama across the Caribbean, to the USA and then East-NorthEast to the Azores. From the Azores you would head south to the Canaries and then south west towards South America, and then from South America, usually from Rio De Janiero via Tristan Da Cunha to Cape Town. While you can go from the Canaries to Cape Town, it is nearly 5000 miles non-stop, and not a voyage to take lightly—going from the Canaries to Brazil is usually a much better bet at 3600 miles.
While you could go from Panama, along the South American coast to Rio, I would advise against that. First, you'll be going through some of the more heavily pirate infested waters doing that route. Second, you'll be sailing upwind against the Northeasterly trade winds, with South America as a lee shore, which is not a safe undertaking. Then you'd be sailing south against the Southeasterly tradewinds with the coast again as a lee shore.
Since you're starting out on the West Coast, going the long way around might actually be easier and faster.
Going across the Pacific to the Southern Pacific, Australia and New Zealand then across the Indian ocean to South Africa may make a lot more sense. It would also avoid having to do a Panama Canal Transit, which is getting fairly expensive and increasingly difficult to do in a small sailboat.