Is it possible that they're using the electric WH as an indirect tank? Some models, especially those designed for solar, could do this.
That aside, the first thing you need to do is figure out what your actual heating loads are. There are ways to do this that aren't onerous, and it is required to decide on what is the best fit for you. Generally, NG will end up being less volatile in pricing, and probably less expensive, so I'd plan to go that way when replacing things.
If you can accumulate your oil usage and then get the heating degree day info for your area, you can calculate how many BTU's you actually used. Then, you can relate that to a good approximation of the size of the boiler you need to get. You'll probably find that the boiler you have is at least twice as large as what you need, and maybe even more.
Radiators work quite well at lower temperatures than baseboard, and lend themselves to a modcon boiler. The lower the temp you can supply, the better the efficiency, and a modcon can adjust the burner size to accommodate your needs IF and only IF you size it properly. If you also then install an indirect WH, your boiler won't need to maintain temp all year long, further increasing your efficiency. With mine, in the summer, it generally only runs maybe once in the morning after baths, then cools off to ambient for the rest of the day. Much more efficient than running and maintaining temp for that occasional hot water use. A modcon can survive with cool returns. You may find that for many days, it could run in the 130-degree range and keep you perfectly comfortable and be reaching in the mid-90% efficiency range. You can't lower the temp of what you have because it needs to be hotter for the hot water issues, plus, that low would put it into condensing range and the burner byproducts combined with the moisture would eat it up along with the flue.
As to brand, it's more important to find an installer that can put it in properly and adjust it for your real needs. I ended up with a Buderus unit, partly on recommendations, and partly because their US headquarters is about 15-miles from my home, but there are a lot of them out there that could serve you well.