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So one of the ideas I've come up with for system to system travel, in the early colony stage of my world, is using fuel boosters to start the journey and then to reach the required speed for the colony ship to reach the next system, using solar sails.

Is this a plausible mechanism for inter-system travel?

The storyline will be making no use of hyperdrive/wormholes etc, however later on there will be the use of anti-matter/ion drives. But this is for the expansion era of the story.

I was thinking the original colony ships in my timeline would involve some 'sketchy' at best cryo sleep with occasional failures. The technology would have been developed as an alternative to riskier medically-induced comas.

I'm aware that the time required to traverse from one star system to the next would be quite large. But this age of expansion (in my universe) would be what sets into place the colonial divides in religion/science/design and political views.

It was covered in a comment, but the answer is

Yes

A solar sail is a perfectly viable method of travel. It will be very, very slow, but there's nothing inherently wrong with it. Given the distance between potentially inhabitable worlds in our galaxy (yours might be different, of course), you're talking centuries (at least!) of travel, so cryogenic hibernation is basically the only viable option if you want someone to make the trip personally, rather than genetically.

To be clear, the maximum velocity theoretically achievable by a solar sail lightcraft is circa 0.11c, so travelling to the nearest star would take around 40 years. This speed is only achievable with power beamed from the starting point using a 1000km-diameter Fresnel lens. Using solar power alone, the approximate exit speed would be 0.005C, and the trip would take 800 years.

This is to the nearest star. If we assume at least 100 ly separation between solar systems with habitable planets (and here we're likely being very generous), we're talking forty thousand year trips. That is, for reference, longer than all recorded history - the oldest cave paintings are about 40 000 years old. You'd definitely get some political divides, though, given that two thousand generations would have lived and died before the travellers made it to their destination.

How about solar sail brakes?

The thing about going fast is that you then have to slow down, somehow. Consider the sail. The sail provides more acceleration the more solar wind it can catch. The farther you are from the star, the less dense the solar wind. Solar wind pretty much nonexistent in interstellar space.

But as you reach the destination you are going towards the sun of that system. The solar wind gets more and more energetic and the sail provides more and more backwards acceleration.

My proposal - use your fuel boosters to get up to full speed and then the solar sail to slow yourself down at your destination.

When designing interstellar travel techniques, the thing to remember is that constant acceleration is the key. Low reaction, constant acceleration is interstellar physics' version of compound interest; using less fuel to add less acceleration over a longer time period works out in your favour, especially as it would appear these engines are usually more efficient in terms of energy output against their fuel.

Ideally, you'd only use rocket boosters to escape your local gravity well (IE get off the Earth) and then use your sails for the entire remainder of the journey. If your two solar systems are adjacent, then this works particularly well because for the first half the majority of your solar wind is coming from the sun, speeding you up, and for the second half it's coming from your target star, slowing you down.

Ion and plasma drives are a thing, and worth looking at as your next generation of engines as they're currently being looked at by NASA.

The one type of engine that you can guarantee won't be used for interstellar travel will be standard chemical rocket style propulsion systems, as for the distances you need to cover in interstellar travel, they are way too inefficient and you don't get that benefit of sustained acceleration over time.

In this case, to reach any destination in the shortest time possible, they would use all the best combination of methods. One combination I can think of is use chemical rockets to escape the planets gravity well and head straight for a slingshot around the sun. Once you are escaping the suns gravity well, the solar sails are deployed, thus maximizing the highest concentration of solar winds to push you. Once the solar pressure dies off, lasers are then shot at the sails to continue the acceleration.

Upon arrival on the other side, you wont have most of these available to you, however Willk above has a good idea.