For batteries I have been using Halfords HB063, but I have a tradecard so price is good.
063 batteries fit, but the terminals are near teh bulkhead, still the correct way round so battery leads fit. In addition, terminals near the bulkhead mean they are away from the battery clamp.
Alternators are a bit more efficient, and charge a battery faster. But if the dynamo is working, I would leave it.
To fit an alternator teh first issue is finding a quality item, there are so many poor quality repro or "recon" ones sold (record for me was a new Lucas recon lasting about 150 miles)
Ideally a later spitfire mounting bracketry. The control box is no longer used. The F+WL wires need joining, the earth wire is unused, all the other wires need connecting together.