Here are some potential options. These will depend on your budget, and your skill level: Are you good with a soldering gun?
Your set is a low cost set with a DC powered only plastic body locomotive. Either it is a 0-4-0 dockside switcher with a number of maybe 8705, or a smaller steamer (2-4-0) with an engine number of maybe 8625 or 8902. Meaning you can not use a transformer: You need to use a DC power pack to run your trains.
As mentioned above, the DC power pack Lionel used in these sets is really an HO type power pack with very little amperage. You could buy a bigger, more powerful power pack. But unless you buy one specifically for G gauge trains, they all will still have a lower amperage. HO trains don't need the reserve power our larger O gauge ones do.
1) The easiest thing to do would be to get another smaller 45-50 watt starter set type transformer to use for your accessories. These can be found at train shows fairly cheaply. You could go lower than that (like a 25-25 watt version) depending on what you want to power off it and how many items. If the items are all "momentary" like your whistle (though it does have a light), the real small transformers are usually the cheapest because they have little sales demand. If you're planning on adding more things to this accessory transformer, like lights - it'd be better to go with something bigger.
OR get a couple of the small transformers. The nice thing about this method, is you can custom adjust the voltage to the accessory for optimal operation, versus the more popular larger Lionel transformers that have fixed accessory voltage.
2) My favorite transformer of all time is the Lionel 1033. The B-U setting of 0-11 volts would be perfect for running your train. BUT you'd need a conversion box made by Lionel (for their line of large scale DC trains) at one time for running DC powered trains with an AC transformer. You could make an improved version of this yourself depending on your skill level. You can find a good condition, serviced 1033 for under $75.00. Even less. But it'd be good to ask in advance if it's been serviced.
3) Or if you can't find the Lionel conversion box (they haven't been made in years... e-bay would be the place to look for that), if you have a locomotive with a tender, you could put a regular at-one-time-standard electronic circuit board reverse unit in the tender, with a tether cord to the locomotive - depending on your skill level. Lionel parts dealers will have this board for around $20.00. In the mid-1990's Lionel did make the plastic body 2-4-0 steam engine just this way. The circuit board allows you to run the engine with a normal transformer and gives you forward-neutral-reverse operation.
4) You could wire in a small bridge rectifier into the engine which would allow running with a normal AC transformer, BUT it would be forward direction only.
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It's a long story, but I went with the second option. I have both AC powered and DC only locomotives like yours. I prefer to add more weight to the DC only locomotives versus a circuit board, so that I call pull longer trains. So I set up my wiring so that I can either run my layout on normal AC power or rectified DC power. Actually some of the low cost engines (even if they have a circuit board reverse) just run better on the DC power.
By the way, I'm not at all knocking your train engine. I like those DC powered steam engines. They're affordable, easy to modify, easy to improve, run on tight 027 curves, and add some visual variety to a layout. My real favorite is the 8500, which did come with an AC motor but manual on-engine reverse only. So I swap out the AC motor frame with a standard DC one.
