So, wading in with all guns blazing it is.
Algae are plants, they are just more primitive than the type of plants that we actually want to take up residence. There is no chance, or desire really, to have an algae-free tank. Algae perform useful functions. What we want is an environment where the algae is under control. Algae gets out of control because it is more able to rapidly adjust to changes to its environment; These changes are especially prevalent when our tank is immature, as yours is. When the plants adjust to these changes they will out-compete the algae for access to the nutrients available and thus naturally limit the growth of algae.
The way we approach this with a new tank is to select easy to grow vigorous plants such as Hygrophilia polyspermia or Elodea densa or Cabomba caroliniana or Ceratophyllum demersum or others. These are plants that don't require large expensive light fittings, specialist substrates or great skills to flourish. They will however, grow quickly and keep algae growth to a minimum whilst the rest of the habitat is maturing. Later, if you desire, you can whip them out and replace them with something more challenging as your skills evolve.
My tank is placed in a room with lots of Sun, that's the way our living room is with lots of glass, so...
This is probably the biggest problem you have. There are only two solutions. Move the tank or shield it with blinds or some similar arrangement. Failing either of these it is more important than ever that you produce a thriving and vigorous plant mass within your tank. Probably the last thing you require are fancy-dan "daylight lights". It is also important that you pay especial care to limit the lighting period of your lighting to give the plants a "dark" period. Limiting the amount of light available in this manner also helps to limit the amount of light delivered to the algae.
I've started adding algae stopping liquid
Algaecides are not the solution. They can introduce more problems than they solve. All the dead algae ends up polluting the water column with ammonia as they decompose. Not what we wish for when performing a fish-in cycle as you are.
...and have removed the existing plants.
Strong plant growth is the primary algae suppressant in an aquarium so you should really replace them.
Currently soaking wood and plan to get plants that will grow on there so I can remove and clean.
You are unlikely to achieve the sorts of growth levels required by using plants that attach to wood. These tend to be fairly small slow growing species.
May consider ultraviolet light through the filter.
UV may be an effective treatment for algae. However it can work as a suppressant to a fishes natural immune system if used for prolonged periods.
Disturbed substrate tonight to see level of cleanliness.
Unless you are vacuuming your substrate you should limit the amount of disturbance to it. The reason is that you tend to lift all the nutrients that are held in your gravel into the water column where the algae can utilise them. This can often cause algae blooms. These nutrients come from two main sources; uneaten fish-food and fish poo.
Finally ("at last" I hear you say) I feel that it is important that you start to think more critically about the advice you are receiving from your shop. You seemed to be pleased with the advice you have received from them according to your initial post. From my point of view, you have been grievously misled.
Regards Steve.