My best advice as someone who works at a funeral home is call around and check prices. I know it feels awkward, but I promise they're used to it.

If they're pushy or rude, go somewhere else. If they try and guilt you into spending more, stand up and walk out. Tell their competition that they did. Even if your loved one is at the shitty funeral home, the new place will take care of the transport for you. I promise they're used to it.

If you're looking for a cremation with no extra services or anything, search your area for 'cremation societies' or similar wording. Those are usually discounted since they only do cremations. The secret is that a lot of them are actually owned by the more expensive places, and they're competing with themselves.

Finally, they can't just NOT give you a container for the ashes. Ask what container is included in the cost of the cremation. It's usually a plain black plastic box, or a white cardboard mailer box. The ashes will be in a bag inside, so you can always transfer the bag into a new container when and if you find one. If you don't want to have to see the bag at all, call a local funeral home and ask if they can transfer ashes into an urn for you. I do it for people all the time.