“No problem,” I thought. “I’ll just connect through my Pixi Plus.” Two minutes later I was back online.

If you too must have an Internet connection before you can get anything done, Palm’s (PALM) new Pixi Plus smartphone is worth a look. Along with the Pre Plus, it goes on sale Monday, operates on Verizon’s (VZ) much-loved wireless network, and in a pinch either can act as your wireless lifeline, sharing a high-speed data connection with up to five laptops or other devices. The Pixi Plus will be $100 and the Pre Plus $150, each after a $100 mail-in rebate and a two-year Verizon Wireless contract.

Besides being a portable wireless hotspot, the Pixi Plus is also a pretty cool phone. I haven’t had it long enough to give it a comprehensive review – it just came in the mail about 24 hours ago – but I’ve already spent enough time with the phone to come to three firm conclusions.

First, I like the Pixi’s hardware design better than the Pre, which was already a good smartphone.

Second, Palm’s webOS software is very good – at this point it’s more polished than Google’s (GOOG) Android operating system, in my opinion.

Third, Palm’s still miles away from catching Apple’s (AAPL) iPhone, and even Verizon’s network won’t close the gap very much. The new Palm phones on Verizon could, however, tempt would-be BlackBerry and Android buyers to go with Palm instead.

Let’s take a closer look at the Pixi Plus, starting with the “Plus.” Palm already had a phone called the Pixi that operates on Sprint’s (S) network. So what makes this version a plus?

WiFi. The original Pixi didn’t have built-in 802.11, a big shortcoming that made it less desirable than its older sibling the Pre. This version not only has WiFi, but puts it to unique use: an app called Mobile HotSpot shares the phone’s Verizon broadband connection with other devices.

Before you get too excited about that, though, here’s some fine print: Using the feature will cost $40 per month on top of your standard voice and data charges, which for me would be a deal-breaker. (Verizon’s smartphone voice plans start at $40/month for 450 minutes, and the data plan is $30/month for unlimited data.)

In other words, Verizon has set this up so that you pay more to share the phone’s data connection than you did to get the connection in the first place. Why would Verizon price it so high? Because the company doesn’t want too many people to use the feature and overwhelm its network. (There are other downsides, too: One is that you can’t share the wireless connection and take a call at the same time. Another cropped up in my testing; though you can supposedly connect up to five devices at once, the Pixi dropped my iPhone’s connection when my computer started streaming video.)

Even without the WiFi trick, there is plenty to like about the Pixi Plus.

Because of its uniform design the Pixi has a more solid, upscale feel than the Pre. (I’m not a fan of the Pre’s slide-out keyboard.) The packaging is sharp, evincing a Cupertino-esque attention to detail. The Pixi has a 2-megapixel camera with an LED flash, swappable back covers, a comfortable keyboard and Palm’s excellent webOS software.

Palm has crafted its phones to be true denizens of the cloud: About five minutes after I took the Pixi Plus out of the box I had loaded all of my contacts, calendars and e-mail into the device. It was so easy because I use Microsoft (MSFT) Exchange Sync through Google Apps for all of those services, so loading the data was as simple as logging into my account. Still, Palm deserves credit for making the process very smooth. Not only are Palm’s phones easier to set up and customize than the iPhone, I would argue they are easier to set up on Google’s services than even Google’s own Android phones.

Not everything about the Pixi Plus was wonderful, however. I didn’t have time to thoroughly test battery life but it seemed to be just average. The interface wasn’t quite as responsive as my iPhone 3GS. Web browsing was fine, but slower than the iPhone when both were using the same WiFi connection. And of course there’s the matter of apps; the iPhone has 10 times as many, and they’re generally higher quality.

My biggest beef with Palm’s phones, though, is the screen size. The Pixi has a 2.63-inch screen, compared to the iPhone’s 3.5-inches. In real life, the viewing area on the iPhone is roughly 50% larger. Even though the resolution on the Pixi makes things very sharp – 320×400 to the iPhone’s 320×480 – there are things you just can’t do on a screen that small. Like read a Google Voice voicemail transcript without a lot of side-to-side scrolling. Or view a calendar in month view with some detail on individual appointments.

Palm seems to have made a calculated decision to target BlackBerry users and folks who loved the original Palm Treo, so the screen has to shrink to make room for a keyboard. I get that. And I get that there are a lot of people who refuse to even look at a smartphone that doesn’t have a keyboard.

But I still think Palm needs to bring us a phone with a nice big touchscreen, and soon. Mainstream consumers are getting more comfortable with on-screen keyboards by the day – and I would argue that cutting-edge mobile apps like 3D games, navigation services and video need the screen real estate.

Until now, Palm has had a first-rate mobile operating system hidden behind small-screen phones on Sprint’s network. The Pixi Plus and Pre Plus address the network issue. Now it’s time to really upgrade the hardware.