There are a lot on Ebay but if past experience is any light on Roman coins then there are a lot of Chinese fakes. Where is a good reputable but reasonable place to buy a few Roman coins?
I'd start at Vcoins probably.... https://www.vcoins.com/ Also, use the advanced search for type and filter by price.
Depends on what you want to buy? Most get their feet wet with some inexpensive ($1-5 each) late Roman bronzes ("LRBs") - Constantinian, Valentinian, and Theodosian dynasties. If you steer clear of sellers in Cyprus/Bulgaria, there are negligible examples of fake LRBs on ebay. If you are wanting a nicer first coin, like a silver denarius of Trajan or Marcus Aurelius, I would recommend hunting around for a ~$50 example with high eye appeal on Biddr or Agora Auctions. Just be mindful that most auction firms charge 15-20% on top of all winning bids, and most charge $10-20 for shipping because they don't ship uninsured. Vcoins is another good venue, but all of their listings are fixed priced, and frankly, 75% are way overpriced. I personally wouldn't recommend dropping much more than $50 without having a solid idea of what you're interested in.
Frank Robinson at www.fsrcoins.com and Dr. Ronald Kurlan out of New Jersey (does not have a web site).
This thread is a good place to start: https://www.cointalk.com/threads/ancient-coins-beginners’-faq-thread.324858/
Finn235 is correct that many coins on VCoins are overpriced, but you can easily get around this by seraching for a coin, say "Trajan denarius" and then listing the order of the coins by "Price: Low to High". You'll see a lot of junk at first, but keep scrolling down until you see one of the quality that you desire. Chances are it's reasonably priced.
You did well, congrats! I hope these are the firsts of many. You got the Caracalla for a fair price and the Diocletian for a great price! But what matters are the coins. Both are in good condition and will be excellent places to start and will provide lots of learning opportunity.
Congratulations with the new coins. I still have my first Roman. Not so pretty but it was a gift. My first real buy was a fake. 2nd too.... ouch. Hope you will keep on collecting ancients.
Next time highly recommend you browse the inventory of our fellow member @Ken Dorney who has one of the finest shops on vcoins with stuff for beginner and intermediate collectors. His direct link is http://coolcoins.com/ Another dealer I highly recommend for beginners is Marc at https://mrbcoins.com/ On both sites you'll find a lot of budget friendly options for beginners. These two dealers also price their coins well, so you'll have fun shopping and save some money. And also, contact our very own @John Anthony ....he is the king of getting special pieces at insanely low prices. How insane? He found me a Julius Caesar lifetime Denarius in VF condition for $900. The same coin would have easily been $1,200+ on vcoins or any online auction. Tell him what kind of coins you like or what you're looking for and he'll come back with some great offers. And no, I'm not related in any way to them...just my honest assessment.
Best advice on how to shop at vcoins that I've ever heard. I do exactly the same thing you do, then once I'm finally sure I have the right coin at the right price, I still double-check by comparing it to auction prices.