Canada has a vast land area (it is after all, the second biggest country in the world) but the routes for traveling across it are somewhat limited by geography, climate and distribution of the population (and with the population, the road and rail infrastructure).
Any route for traveling across Canada can be split into three main sections: the eastern, the middle and the western. The middle section is the longest and in many way the easiest to decide, as there are relatively fewest options. The eastern and western sections are more complicated as many detours and alternative options are possible.
Road or rail?
Before you start to plot the route, you need to decide whether you are going to travel by road (whether by bus or by car) or by rail or by some combination of the two.
Traveling by train has major advantages. It's the most comfortable form of overland travel. It allows for a social contact and exchange without being quite the claustrophobic experience that traveling by coach can be. Canada, just like the US has been to some degree created by the construction of the railways and following the railway follows to some extent the progress of the white colonists in the country.
On the other hand, the current Canadian railway is a rump of a service which runs on limited routes with limited frequency. Sleeper cabins are very expensive and as many areas (and always the same ones as the train always runs at the same time) are covered at night, you simply miss parts of the country altogether.
Driving across Canada is a bit of a rite of passage for Canadians and certainly a convenient if a bit soulless (especially in the middle part) way to experience the scale of this vast land. However, one way car hires are very expensive and not that common, and if you don't have your own vehicle, one way hire might be simply prohibitive financially Using ride-shares is cheap but not always easy while coach travel is uncomfortable and not that cheap either.
A combination of rail and road is likely to offer the best experience and best value for money for those wishing to travel across Canada.
The second decision is to whether "across Canada" is to mean genuinely ocean-to-ocean drive, or a drive from Montreal, Toronto or Ottawa to the western coast (or opposite).
Road trip across Canada
Trans-Canada Highway, spanning the whole country from St Johns in Newfoundland to Victoria (and now Nanaimo) in British Columbia, is the obvious choice for the route that is entirelycovered by road. However, a visitor interested in seeing the best that Canada has to offer should adjust the Trans-Canada itinerary to include some spectacular sections not included in the Trans-Canada system.
And thus, having arrived in New Sydney from Newfoundland's New Glasgow, it's recommended that a detour round Cape Breton is made. Trans-Canada doesn't include Halifax nor Lunenburg and both those places in Nova Scotia are well worth a visit (and can be incorporated into a route).
In Quebec the Trans-Canada misses the Gaspe peninsula and follows the south bank of St Lawrence. Taking a ferry from Riviere du Loup and following the north bank will give a more scenic drive (a detour north towards Tadoussac is worth a couple of days if you are not pushed for time) and will include the magnificent city of Quebec.
From Quebec, follow Trans-Canada to Levis and Montreal, and from then on to Ottawa. In Ontario include Toronto (which doesn't lie on the official Trans-Canada) and consider a detour (half-day minimum) to Niagara Falls. Then follow the route to Thunder Bay and via the Canadian Shield to Kenora and then to Winnipeg in Manitoba.
In Saskatchewan, Trans-Canada passes through Regina but route 16 goes through Saskatoon which is a nicer city and with more interest for a visitor than Regina. From Saskatoon go to Calgary via Drumheller with its atmospheric badlands and fascinating dinosaur fossils.
Once in Calgary, follow Trans-Canada through the Rockies as far as Lake Louise, but instead of traveling across the Rockies through Golden and Revelstoke, take the Icefields Parkway, one of the most spectacular drives in the world, to Jasper.
From Jasper, if you are feeling very adventurous and can afford it, you can follow route 16 to Prince George and Prince Rupert, from where in the summer you will take a ferry along the magnificent Inside Passage to Port Hardy at the northern tip of Victoria Island. Drive down the island (detouring to Ucluelet and Tofiono) to Nanaimo and Victoria, from where you take the ferry back to the mainland and the glories of Vancouver.
Alternatively (and much more quickly), cut south from Jasper to Kamploops and there rejoin the Trans-Canada for the final stretch to Vancouver (with the option of crossing to Vancouver Island from there).
Rail trip across Canada (with road detours)
The rail trip across Canada will take you from Halifax to Vancouver, with possible side detours. The first leg is The Ocean train from Halifax to Montreal (there is a connection to Quebec City by a local train too: stop over there). From Montreal, travel to Ottawa, and from Ottawa to Toronto where you will board the flagship service of ViaRail, The Canadian. This will take you through Canadian Shield (north of Trans-Canada Highway) where you can stop for a taste of wilderness in fishing and hunting camps on the way, to Winnipeg and Saskatoon in the prairies. From then the train goes to Edmonton rather than Calgary and on to Jasper (where a side trip on the Icefields Parkway is possible by coach). From Jasper to Kamloops and then to Vancouver complete the rail trip.
Whichever way you choose, budget more time than you think you'll need. Canada is unimaginably vast, and the distances are huge. If driving, plan your stops carefully and make sure you have enough fuel, food and energy reserves for all this driving.