First it depends on your 'home' citizenship/passport. Different nationalities have different procedures.

Assuming you have a UK passport -

- Business or Tourist Visas can only be applied for in your 'home' country - although some Far East RUS embassies might vary this, but there is no rule.
- Transit visas are usually obtainable at the Embassy of a neighbouring country or a flight origination country, invariably in the Capital city.

Here is the WebSite of the only UK people who handle Visas applications for the RUS embassy. Russia Visa Information - UK - Home Page
Most of your questions can be answered here but if anything is unclear ask here again.

Transit Visas are really intended for changing airports while flying elsewhere or train journeys starting and finishing outside RUS but entering RUS territory. I have heard of them being obtained by road travellers but only for very short periods that are based on a daily distance between your stated entry and exit border. I think it is worked out as something like 500km/daily.

The best/easiest is a Business Visa as it cuts down on paperwork required such as confirmed accomodation.

Ensure you have sufficient time on your Visa as they cannot be extended within Russia and overstaying, for any reason, can cause problems, delay, penalty and costs.

Medical Insurance is not required by UK Passport holders as emergency treatment is covered by recriprocal arrangements with UK.

Road insurance can be bought at borders and it is permitted to drive/ride to nearby towns to obtain it (cheaper!). It is only minimum level insurance to comply with the Law.

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