Cisco Core Switch upgrade questions

I'm looking to upgrade our Cisco core switch. it's an old 3560 catalyst with a pretty basic configuration. The existing 10/100 ports are split up into VLANs for various client and server groups. The switch is largely there for routing. There are a combination of static routes and BGP for our connections to branch offices. The current north and south connections are all 1Gb Ethernet and a combination of L2 switches from various vendors (Dell, HP, Cisco whatever was available when others purchased). The configuration on this switch rarely changes. I'm talking one config change every 3-5 years. For this reason, it's gone largely ignored.

I'm hoping to change that with a core switch upgrade and have a few questions.

We are a medium size business. We are very flexible on budget. I want something that is easy to configure, deploy, and maintain going forward, so that it doesn't go ignored in the future. I have plenty of networking experience, so am comfortable configuring a Cisco, even if I haven't had to do so in over a decade. My only lack of experience is with managing BGP, as it's something I rarely have to engage.

1. Cisco site is recommending the upgrade path from a 3560 to the 9300. Does this upgrade path sound fair, overkill, or lacking?
2. With this upgrade path, would I likely be able to copy the config line for line on to the 3560, reducing configuration and implementation time.
3. There was a previous concern among the decision makers that Cisco licensing is difficult and overpriced. Is that true nowadays?
4. Are there other vendors we should consider? I figured transitioning to a different vendor would greatly increase time to implement. Not a deal breaker, but hoping to implement something sooner rather than later.

Any feedback or suggestions are helpful. Thanks!