If there is no lien on the property regardless of whatever "type" of mortgage you take out, it will be a first mortgage. A first mortgage refers to the lien position. A Home Equity Line of Credit or HELOC, if the only loan on a home would be a first mortgage.

Certain mortgages are exclusively structured to be in first lien position, meaning if first lien position was not available, it would have to become available before you would qualify for this type of mortgage. When most people discuss first mortgages, they are discussing programs that require first lien position. These offer the best terms and most attractive rate and fee structures.

HELOCs do not require first lien position, and are actually structured to take 2nd position behind a 1st mortgages; that is not to say a HELOC would not happily take first position. The point is, because HELOCs are designed for 2nd position they are designed to weather the inherent risk associated with 2nd position. To offset this risk, they charge higher rates which is why 2nd mortgages have such high rates. As for trying to get a HELOC with better terms because it will be in first position... don't get your hopes up, I do not know a single lender that will rewrite their guidelines to accommodate a simple second.

What I recommend is looking into a cash out refinance. This is a first mortgage, it will have a fixed interest rate and no prepayment penalty. If you leave a substantial amount of equity in your home, you will not be penalized for taking cash out. Forget about the home equity line of credit. Secure a 30 year amortized fixed mortgage for whatever amount you need to sustain the property for a specific period of time.

Keep in mind your exit strategy, and how you plan on paying the loan back. 

I would recommend that you apply for a first mortgage and not a 2nd-since there is no 1st yet. The fees are higher on the first but the rate is higher on a FIXED rate equity loan. Lines of credit are based on the prime rate which is low currently, but that changes every time the Federal reserve changes rates. 

It is unclear from your question if you are also seeking cash out for ANY purpose other then paying the taxes so I will answer it both ways.

If ALL you are doing is paying the taxes and the having the closing costs rolled in to the loan then you could very likely make the case to the underwriter that it is NOT a cash out transaction and avoid the additional fees, the one thing that may come up as a result of only paying the taxes is that you may get an add on fee for too low of a loan amount. Most mortgages under $50k (and with some programs even higher) have some type of fee added to the cost due to the loan amount.

If you DO need to pull cash out the best thing to do is to pull it out, pay the cash out fee (or absorb it in the rate through rebate pricing) and most likely that will put you at a high enough loan amount that you don't get hit with BOTH fees. Your loan consultant should be able to go over all this with you when you apply but definitely look into trying to do a 1st mortgage as you can obtain a very low (historically speaking) FIXED rate. even if there are some adjustments to your program.

Rates on equity lines are actually lower than first mortgages right now, however they do have the risk of going higher in the future so the answer I would give you depends on how much you need to borrower and how long you think you will own the home as well as how quiuckly you would want to pay it back.

While a 1st mortgage loan would give you a fixed rate, if that is the type of loan you choose, how much you want to borrower would impact the rate you pay, not to mention your closing costs on a first would be higher than what you pay for an equity line, in most cases by a couple thousand dollars.

In addition, the equity line could be accessed for needed funds in the future, depending upon how much you borrower and use while you have it.

All of these factors should be considered when making this decision.

Hope this helps.